Cumrun Vafa

Zierler:

Okay. This is David Zierler, oral historian for the American Institute of Physics. It is March 25th, 2021. I'm delighted to be here with Professor Cumrun Vafa. Cumrun, great to see you. Thank you for joining me.

Vafa:

Thank you, I'm happy to be here today.

Zierler:

All right, so to start, would you please tell me your title and institutional affiliation?

Vafa:

I’m the Hollis Professor of Mathematics’ and Natural Philosophy in the Physics department. I'm at Harvard University.

Zierler:

And we should emphasize that Mathematicks is spelled with a k.

Vafa:

Yes, yes.

Zierler:

Do you know what the special reason is behind that? I guess this is because this is a chair that goes back a long time.

Vafa:

Yes, I believe it's the oldest chair in science in the whole US, and it was established in 1727. And it was at the time where this was the way that mathematics was written in the Latin.

Zierler:

When were you named to this chair?

Vafa:

I think it was a couple years ago. Two years ago, or so.

Zierler:

Cumrun, a question that everybody is dealing with right now, and I'm particularly interested for you because you're not working in laboratories that necessarily need on-site, interpersonal interaction, but still, the way that you work, the kinds of interpersonal relationships that you rely on in your collaborations, how has the past year in the pandemic been with the mandates of social and physical isolation?

Vafa:

Well, a lot of what we do in theoretical physics is thoughts. And so, my area does not need the lab equipment. We don't ourselves do the direct experiments, so therefore for my kind of physics, a lot of it is virtual in a sense anyhow. Though, so a lot of things have gone on as usual, you know, giving lectures, collaborating with colleagues through Zooms. Other than, as is the case for many other colleagues, that the random interactions that occasionally trigger new ideas, which seem to be in some sense the major driver of creativity in many ways, is missing, or at least reduced to a great extent. And I think that is something I have also felt. I should say, however, that in the past few months, I've begun to find a way around it by organizing structured but random interactions with my colleagues. So, I'll just say, "Well, let's meet at such and such a time to just touch base, topic open. Let's not say the topic." So, it's kind of trying to create that random environment as much as we can through Zoom. So, it's beginning to change a little bit that way, but I hope we don't have to get to that normalcy. I think I hope to go back to what it was before pandemic.

Zierler:

Have you found over the past year that you have more bandwidth to work on maybe some long-standing problems that you might not have gotten to otherwise?

Vafa:

Long-standing, I'm not sure. I would say that the nature of the problems I have been working on has not dramatically shifted. It is similar to what I was doing before and continuing. I would say that the main thing which has changed is having the ability of seminars all around the world. First of all, hearing, and also delivering lectures in different places, much more easily. So, in that way, I would say that the situation has become more uniform for all over the world. It doesn't matter where you are, you can listen to everybody anywhere, anytime that the lecture is being delivered, because it's all available to everybody. So, in that sense, it's very democratic, I would say.

Zierler:

Cumrun, just a question for right now, a snapshot, what are some of the most exciting things that are happening in string theory? Here we are, this is a capsule in time, March 2021, what are some of the things that are going on right now that are most exciting and intellectually compelling for you?

Vafa:

Intellectually compelling for me versus what's going on in string theory are two different questions, not necessarily the same. Because what the majority of string theorists might find exciting, I might find not as exciting and vice versa. So, I will tell you what I find exciting particularly. What I find particularly exciting is the ability or the gradual recognition that understanding what constitutes a quantum theory of gravity, and the requirement that it imposes on consistent matter that can arise in such a theory, is becoming more clear. That there are very strong constraints coming from just having gravity around. And this kind of realization, which has been going on for many decades, has become more and more clear as time has evolved. And by now, there are a number of principles that are emerging. This is called the Swampland program. We try to delineate what are the few theories that cannot be possibly arising in a quantum theory of gravity and belong to what we call the Swampland. And what are the good ones, what are the possible good quantum field theories of interactions of matter and forces, which can arise? And that's what we call part of the landscape. So that's my area of interest which I find most exciting. There are, I would say that if you ask more broadly what people are excited about these days, I would say a number of people have been continuing to be excited about the ideas related to holography and black holes and the information puzzle, and some progress is happening in those directions as well. But even though I have worked on that in the past, currently my interest is more focused on what I call the Swampland program.

Zierler:

Cumrun, I'm curious about this idea of the Swampland. Where did this term originate, and how may or may it not be responsive to some of the critics of string theory over the years?

Vafa:

Well, I coined the term Swampland in 2005. So, the idea that we can come up with principles which distinguish good theories from bad theories, or trying to distinguish them by some criteria, was at least it formally started in 2005. Though there were ideas of what could not be possible in a good quantum theory before then, but I think since 2005, there has been this effort to try to be more systematic and try to understand more deeply what these principles might be. So that's the origin of that, and it has been one of those areas of string theory which has been growing rapidly in the past few years. And it is becoming a web of relations and conjectures that some of them have a lot of backing by examples we know in string theory. Some of them have connections with black hole questions, like unitarity of black hole evaporation. The relation between this and how it leads to restrictive features of the wide class of compactifications of string theory is part of this program. So, there's a list of all these conjectures that are emerging, and there's interrelationship and all of that. It's quite fascinating, and we're trying to get a basic idea, what is quantum gravity? What can we mean by consistent quantum gravity? What it is all about. So, trying to get to the basic core and principles of string theory, or more generally what we could call quantum gravity, is the aim of this program. And your second question was what do the critics- what the critics might say?

Zierler:

In terms of the Swampland, I was curious if the use of the term Swampland, which might have sort of negative connotations about going into an intellectual area where you can't necessarily come out, or where you don't really know where you are?

Vafa:

Oh, I see, I see, okay. So, I have to explain the background for this more clearly. So, quantum field theories, [which] can describe the matter and the gauge fields consistently, have been studied in physics for the past, I would say, I don't know, sixty or seventy years. And so [we] understand a lot about it. But one thing we have learned is that there are infinitely many of them which are okay. They look consistent, they look nice, and so forth, and they are very non-trivial and good. But only one of these belongs to our universe. So, the question was, and has been, whether or not gravity would pick one or two or a finite number of this infinite set. And if it didn't, then so be it. It could have been like that and the universe that we live in [is] one of them and that's it. But what this Swampland program is telling you is that almost all of these would-be perfectly fine-looking quantum field theories become bad and belong to the Swampland, if you include quantum gravity as part of this mix. So, in other words, quantum gravity throws almost all of these theories, into the Swampland, and only a finite number- a few, it could be a huge number, but still a finite number of them survive this and they belong to the landscape. So, Swampland in this case is a good cleansing operation. That is, you are just saying, these are the good ones, like with jewels. You're picking these jewels out of this infinite landscape which is mostly incompatible with quantum gravity.

Zierler:

Well, Cumrun, let's take it all the way back to the beginning. Let's go back to Iran, and let's start first with your parents. Tell me a little bit about them and where they're from.

Vafa:

My parents were born in a city called Zanjan in Iran, which is a Turkish-speaking region in Iran. My father in moved to Tehran and grew up in Tehran, after he was six years old. And my mother till I think she was still in Zanjan. But then my father came to the U.S. to study after getting his bachelor's degree in Iran. He came to the U.S. to study in Indiana University in Bloomington. He got his master’s degree in economics and [his] PhD in education. My mother came also to the U.S. to do some studies, but she met my father through my uncle who was my father's friend and they married, and then they moved back to Iran. My mother continued her studies in English in Iran and got a bachelor's degree there in Iran. And that's where I was born in 1960, in Tehran, Iran.

Zierler:

Now you said your parents came from a Turkish-speaking area?

Vafa:

Correct.

Zierler:

Were they ethnically Turkish?

Vafa:

Azeri Turkish language, yes, but not Turkish as in Turkey, but Turkish as in Iranian Turkish minority.

Zierler:

And what language did their families speak?

Vafa:

Azeri. Azeri Turkish.

Zierler:

When did they pick up Farsi?

Vafa:

Well, you know, in Iran they speak Farsi all over the country, so they were exposed to Farsi all throughout their life, but their mother tongue, both of them, were Azeri. They would speak Azeri Turkish with each other. My parents still do speak Turkish with each other, but they spoke Farsi with us.

Zierler:

So you didn't understand that language when they were speaking?

Vafa:

Well, we understood the language because we learned that it's good to understand what they're talking to each other! But we couldn't speak it well. So, I think we have learned a little bit of it in that way, but the language, our "mother tongue" is Farsi.

Zierler:

Are there religious or significant cultural differences between these peoples and the Persian people?

Vafa:

I wouldn't say so. I would say culturally, they are very similar. There's nothing majorly different between them.

Zierler:

Including the Shia religion?

Vafa:

Yeah, the religion is the same.

Zierler:

What were some of the key ethnic or religious or cultural markings of your family growing up that you remember?

Vafa:

Iranian population by and large is Muslim. Mostly Shia, by a huge margin, and so was my family. So, I don't think there was anything distinguished about my family compared to the general population in Iran.

Zierler:

What neighborhood in Tehran did you grow up in?

Vafa:

A place called Shemiran. Shemiran is in the northern part of Tehran, and it is by the mountainside- well, closer to the mountainside. And it was one of the nicest areas I would say in Tehran. It still is in some sense one of the good areas in Tehran, even after so many years. And yeah, so that's where I grew up, in Tehran. Well, I was in that area for all of my- until my adulthood in Iran, except for six months where I came to U.S. with my father, who was doing some training program in Washington D.C. in 1963, so I think at that time I was around three years old, so I came there. I have vague memories of being there in D.C. for six months. I remember some recollections here and there like pictures in my mind, but later I learned that was the same period that JFK was assassinated. We were there in D.C. I'm told by my mother that when I came back to Iran after those six months, I didn't speak Farsi anymore. I only spoke English and then again, I forgot English and I only spoke Farsi (laughter). So I've changed my tongue a few times (laughter).

Zierler:

Cumrun, how would you describe your parents' politics growing up? Were they supporters of the Shah?

Vafa:

My father was always liberal, I would say, in terms of emphasizing democracy and so on to us. And he was always, even though he worked for [the] government at a high position. His last post in the government was Iran's Ambassador to the European Common Market in Belgium. He was always hoping for democracy, and he was hoping that the policies that the Shah is pursuing is going to go towards democracy, but each time it was continuing, my father was getting more and more disappointed it's not going in that direction and was sharing his disappointment with us when we were growing. So that was the politics. My mother didn't talk too much about politics with us.

Zierler:

Cumrun, when did you start to get interested in science? Was it early on?

Vafa:

I was interested in science when- well, it depends on how you're counting "interested" but I think I was second grade primary school. Like eight years old or so, I just remember looking at the sky and pondering about the moon and why it's not falling. And I think that I remember even asking people around me, you know, why is this thing up there and what's keeping it up there? Why is it not falling? And so on. And I would be hearing answers like, "Well, there's this mysterious gravity force that keeps it up there," and so on. I didn't know what that meant, and what is that supposed to do, keeping something up there? So, I was curious, but I remember also when I was in third grade, that's nine years old, I distinctly remember this, that our teacher was teaching us about the concepts of width, height, and depth. So, she was saying there are these three things, width, height, and depth. And then I asked myself, why three? Why do we have three? Why do I have to remember three concepts? Why not more, why not less? I was kind of puzzled by that three. Of course, I didn't formalize it to the notion of dimension, but it was kind of a question [that] stuck in my head- these are the kinds of questions that I don't think typical kids necessarily get alarmed about. But I was! Whether you call that interest in science or not, I do not know.

Zierler:

Well, you could say that you were interested in gravity and multidimensional universes right from the beginning.

Vafa:

You could say that. I'm not sure it's exactly accurate, but these are the eight- and nine-year old’s reflections on these things. And then I remember another episode from when I was maybe twelve or thirteen years old. We lived in a big compound where my cousins and other uncles and aunts and so on lived, so it's a very nice kind of setup. I remember playing around and I saw one of my cousins was working. He was older, he was maybe seventeen, eighteen years old. He was working on his homework, and I said, "What are you doing?" And he told me, "I'm trying to calculate where the ball lands when you give it a given velocity." I said, "What do you mean calculate?" He said well I am using some math to find the trajectory of where it lands. I said, "Can you use math to actually find where a thing falls?" He said yeah. I said, "Wow, that's amazing. How could that possibly be true? Just a simple thing, on some paper you can write down and you can say where it's going to fall just by that?" He said, "Yeah." I was amazed at simple math, that you can actually do this to get something conceptual suddenly translate into something real around you. And this connection between mathematical thinking on a piece of paper or whatever and that coming out in reality, was to me an amazing ah-ha moment. Wow, that's amazing. I think that my interest was kind of like on the side, I was continuing learning about science in high school. I was curious about how physics and other things worked, but I was not- I don't think that I would consider the science education I got in high school that great. So, I didn't really think I'm learning much about, you know, amazing physics and so on. Instead I was very attracted to math from early on in high school, and in particular Euclidean geometry attracted me. It was very attractive to me and I would spend hours and days trying to solve problems in Euclidean geometry. The idea that you can start from a precise set of axioms and derive from those theorems or prove certain properties of triangles or circles and things which don't look obvious, you can prove, sometimes by drawing an amazing extra line here and there, and connect these thoughts together, was very attractive. So, math was my major, major interest in high school. And the science was kind of on the side, interesting but it always sounded mysterious, because it didn't come out like something I could hold onto. It was kind of a little bit beyond my understanding. Math I could really understand, but physics sounded like, "Oh yeah, they have found that there are atoms and there are these electrons going in orbits." I remember for example, I was learning in chemistry that there's a hydrogen molecule, it makes an angle, I don't know, 104 degrees or whatever. And I wanted to see why. Why it is this angle? Why is it not 180 degrees, and what is the reason that there is such an angle in the hydrogen molecule? I was trying to see if there's any Euclidean geometry reason for this particular angle. So, I was trying to, given what people had told me about the physics, trying to see if I can understand the mathematical reason for that. Of course, I had no idea what quantum mechanics was, and what kind of techniques people now use to get these kinds of things, but I was just trying to have a mathematical explanation of all these things for myself. I was trying to do it myself. Of course, with no good results at that time. And so, these were the kinds of interests I had. I would say that my first real introduction to modern physics was when I was trying to learn English towards the end of high school, in a more serious way in view of the fact that I was planning to apply to colleges in the U.S. I knew that I'd have to improve my English. So, I got a tutor to teach me English, an American whose name I don't remember, who agreed to tutor me. I should say, parenthetically, that I was always good in English compared to my classmates because I had this background, as I mentioned, I had come to the U.S. when I was a child. So compared to my peers, English was easier for me, but I still wasn't that good, and I always really wanted to learn more English. And so, this was an attempt to really improve my English, and he asked me what kind of books do I want to study? I said, "Well, I don't know. Whatever books in English that you suggest I would study." So, he said, "Well, what are you interested in?" And I said, "Well, economics maybe?" I was interested in it because my father had studied, so I said maybe economics. And then I said also science, I'm interested. I was interested in science as I said, but I did not have a good source of it. And so, he said, "Okay, I'll give you some material for both." I think for economics he gave me a textbook of economics by Samuelson, and for science he gave me, a text, I do not know from where, but it had a chapter on Einstein’s special theory of relativity. In a language more geared towards a general reader. So, it was kind of not a very difficult reading for a high school student with some simple math background. So, reading that special relativity material was really an eye-opener. I really got excited about modern science, and that was one of my first loves, I would say, for science. When I saw that amazing new things are coming out of science in this way. You know, the properties of length contraction and time dilation and so forth, which are simply related to simple things which you can compute using Euclidean geometry, assuming that speed of light is the same for everybody. That the computations were based simply on Euclidean geometry which I loved, I found fascinating. So, I found this connection between geometry and physics in the context of this abstract theory, namely this special theory of relativity, quite enchanting. So that was great excitement for me. And so that was something that I said, "Wow, this is amazing." So, these were my exposures during high school. I remember that I would ask my physics teacher in high school questions that I couldn't get satisfactory answers. So, I remember reading the phrase in my physics textbooks that light emerges from perpendicular oscillations of electric and magnetic fields. That was the phrase, like a magic phrase, that that is light. And to me, this was wow, electromagnetic fields oscillating perpendicularly and that's light. But, what does that mean? So, I wanted to understand more about it, and I would ask my teacher, can he explain more about what this statement is in our book? And he wouldn't know much more about that than that. And he would go on the blackboard and draw some pictures of a wave going up and down. He said, "Well, this is like a heart rhythm. You know, you can see the heart rhythm going up and down when you move on, up and down?" So he would draw a heart rhythm kind of picture on a black board and point to where it's moving and says, "Well, that's what it is." so I didn't get any feeling that I understood any more than just that statement that was in the book. So, I felt always kind of like a disconnect between modern science and what I wanted to know. But math, on the other hand, I would say was completely different. The math was well-taught, was very well-ingrained in us. They taught us really how to prove, how to think things, what are the axiomatic way of thinking about mathematics. And especially in the context of Euclidean geometry. We also had great algebra teachers, trigonometry, and all that. So, the math side was very well-developed. Including modern math, where they were teaching us things like probability, combinatorics and all that. So, the science side, I would say, was not on par with our math education.

Zierler:

Cumrun, if you look at the chronology of when you're thinking about coming to the United States for your undergraduate, in 1977, 1976-1977, was the deteriorating security situation in Iran, was that part of the consideration at all? Or were the motivations purely that coming to the United States was just the best place for you to pursue your education?

Vafa:

There was no such worries about any instability in Iran at that time. At least not that I was aware of. I mean you would hear a few random attacks of terrorists, and officials being assassinated here and there, but nothing as worrisome as a complete turnover of a system. So no, that was not at all in my mind. As we were growing up, we were always hearing from my father about the education that he received in the United States, and how amazing America is as a place to learn. And how amazing America is as a cultural place, and how America is in terms of democracy, and all these things. So, America held a very special ideal for us in terms of a place of learning and a place of tolerance, openness, and all that. So, it was kind of a place that we always assumed, that's where we're going to go for studies. So that's what we were going to go, just like my father had done. For him, it was much more amazing to have done this. I should have explained it more clearly, perhaps. His father did not know how to read or write. My grandfather. Despite the fact that, you know, he was an amazingly rich merchant, but he didn't even know how to read or write. And in that environment, for my father to have not only finished high school in Iran, continuing education in Iran, but to insist and get permission from his dad to come to the U.S. for further education, higher education, is remarkable. And so, I find it very surprising that he first of all was seeking for such a thing, and he did it. And so, with that background, and he was telling us about how amazing this whole education that he received in the U.S. was, and how much [of an] eye-opener it was for him. The education and culture of North America was kind of engrained in us when we were growing up as something that we would love to do when we grow up. So that was an assumption I was always making from early childhood, that yes, I was going to be studying in some colleges or universities in the United States when I grew up.

Zierler:

What advice did you get about where to apply?

Vafa:

Well, I should again give you another background. The official length of the education in Iran (before applying for college) was twelve years. I was in the eleventh grade, I heard that a cousin- my cousin whose mother is American. He was going to an international school, high school in Tehran. Iran Zamin was its name. And we were the same age. So, he was also eleventh grade. And I was talking with him, and I saw him looking at a book talking about preparation for SAT. And I asked him, "What is SAT?" He explained to me SAT is an exam you take for getting ready for colleges in the U.S., you have to pass these exams, or take these exams, and then they take your grades. And I said, "What else do you need to do for applications to colleges in the U.S.?" And he told me, well let's look at it. And there was a list of things at the beginning of that book telling you the requirements for colleges, you know, achievement tests you had to take. Scholastic Aptitude Test you have to take, and some other things. And noticing the absence in the list of the diploma from high school. I said, it doesn't talk about diploma. What about that? He said, "Well, I don't know. Maybe you don't need a diploma from high school." I said, "That's surprising. You can apply to colleges in the U.S. without the high school diploma?" He said, "Well, I don't see any reason. This doesn't say you have to have a diploma." I said, okay. I told my dad I'm going to apply to colleges now (laughter). So that's what I did. I applied to colleges [in] eleventh grade, I took my exams, SAT and Achievement Tests, and I said, "You know what, I'm going to get to college as soon as I can. I'm going to apply to as many places as I can think of." Well, I didn't know many places. So, I had heard about MIT, I'd heard about Harvard. I'd heard about Princeton. And a few of my cousins were in Purdue University, maybe also University of Illinois. Anyhow, I applied to five universities in the U.S., but I also was thinking perhaps maybe it's a good idea even for the last year in high school to come to the U.S. Because I thought, if I'm going to college in the U.S., maybe the last year of high school I could be in the United States and apply directly from there. So, I applied to a high school, it was Andover or Phillips Academy (don’t remember which). So, I applied to that, and they're a boarding school. But anyhow, the one I applied to immediately replied to me saying, "Sorry, we don't take a student in a senior year in high school. We don't accept this." So that was that. So, the high school was out of the option, so I was waiting for other results from the colleges, and I think University of Illinois admitted me. Princeton put me on the waitlist. MIT put me on the waitlist. And Harvard admitted me. So, when I got admitted to Harvard, I said, "Wow, that's fantastic." Despite the fact, I should say, that my SAT score was 320 out of 800, which is remarkably bad. But I guess they also have this Test of English as a Foreign Language (TOEFL), which it is also out of 800, and I got 560, which is not remarkably high either, but okay, I think that passed their lower bound or something. At any rate, 320 SAT scored was ignored. My math scores for SAT and Achievement Tests were much better, so that might be another factor that was not a problem. But anyway, Harvard admitted me, but I did not want to come to Harvard, because I knew, or I'd been told, that Harvard requires a lot of, you know, humanities courses that you need to take, and your English has to be good and so forth. And I was not interested in that. So, I really thought that MIT would be a much better match with my interests. More technical and more mathematical things, perhaps. And I was interested at that time to learn some engineering, and perhaps economics. That was my focus, so I thought, you know, engineering, certainly MIT is better than Harvard. And economics should be good. So I thought it could be great if I can get to MIT, so I pushed MIT telling them that, look, I have got an admission to Harvard, but if you guys give me admission from this waitlist, I'll definitely come to MIT. And lo and behold, that turned out to become an admit, and that's how I ended up at MIT.

Zierler:

So physics was not on your radar from the beginning?

Vafa:

No, no. Not at all.

Zierler:

What were your impressions of MIT when you first got there?

Vafa:

Well, MIT was a very open place. The culture was open. Things were perhaps too open for me. This openness was strange for me, where I had grown in a culture more guarded about privacy and interactions with others. But you know, in general, it took me a while to get adjusted to the culture there. I thought MIT is a typical American culture, which it wasn't. Of course, I didn't know that. But that was my introduction to American culture: the MIT student body! Later I found out it was a very twisted view of what American culture is. It's not the typical culture there. But I got the impression of a very, you know, nerdy and happy environment. You know, people all happily and nicely interacting with each other, and many nice things about it. I remember that it took me like two or three months before I could feel comfortable in my understanding of what was going on in the classrooms. I thought my English was good, but actually I learned very quickly that it was really, really lacking. And I couldn't follow the discussions in the classroom. And it was too fast for me. The rhythm for my understanding English was not the same rhythm that people, the teachers or professors were lecturing in the classroom. So, I was a bit frustrated the first few months. And at the same time, I was trying to adjust culturally. For example, the interaction between men and women, and that's something about how MIT was different from what I was used to. I went to an all-boys high school in Iran. In fact, all the high schools in Iran were essentially just single gender. So, I was not even familiar with that context of interacting between men and women, and cultural issues similar to that took me a while to get adjusted to in the context of MIT. But English was one of the other aspects that I had to get used to. Luckily the courses were easy for me. So, for me, even though I'd skipped one year in high school, it was kind of child’s play compared to what I was used to in high school. Perhaps I should have said more about my high school earlier. It's one of the best high schools in Iran. And it admitted students based on their grades from sixth grade onwards. So, they would come after fifth grade, there's a national exam and based on the score in the national exam, they would select the top people in the whole country. In that case, in Tehran, it was so famous a place that everybody wanted to get into it, and it had the best of the students there. So it was best of the students and it was a very disciplined high school with an amazing principle called Dr. Mojtahedi, who was a mathematician who studied mathematical analysis in France, and came to Iran and after a while, took over to become the principle of this high school, and he transformed it to a very structured and high standard high school, and I owe a lot of the things that I did learn in high school to his management of this high school. And the Alborz High School owes a lot to Mojtahedi, but actually even before him, it was Founded by an American missionary who had come to Iran, called Samuel Jordan. I think he was a graduate of Princeton [Theological Seminary]. He had come to Iran and then he had created this -- His idea was to create a place which was the first college in Iran. So, it was called the American College, or Alborz College, before it was called the Alborz High School. And so, after Samuel Jordon left, then this became Alborz High School, and the remnant of that base is what Mojtahedi took over and really made it quite, quite amazing as well. So, it owes both to Samuel Jordon as well as to Mojtahedi. I owe a lot to the education that was provided, and it was one of the rigorous, one of the best high schools in the whole of Iran. Alborz was very competitive by the nature of the people that they admitted. But in addition, there were like about like 600 students per grade, and they were divided into twelve classes of fifty each. So, the top fifty students were in the first class, and the next fifty in the second class, and so on. And so, at the end of the school year, they would put your grades in front of the school, and everybody would say, "#1 X, #2 this person, #3..." with everyone’s grade in full view. So, everybody would know what everybody got in a public way. So, this was really a very high-pressure kind of environment. Like, there are these 600 students, and you are kind of competing with trying to get the best grades and so on, and so forth. The exams are very, very carefully administered in the form. Again, Mojtahedi administered them, because unfortunately he knew that there would be cheating otherwise. So, he made sure there are no cheating by the students, or favoritism by teachers: wherever you take final exams, all of the 600 students take it at the same time, with the same questions that he posed. And when you write your name on the top of the exam sheet, your name is covered and taped. So, the teacher didn't know whose exam they are grading. So, the whole thing was implemented in a very systematic way so that the exams are graded, and after that they open the names and see which student got which grade, so there's no favoritism. And that was the environment that I grew [up in]. So, this Alborz High School was a quite remarkable oasis, I would say, in terms of the quality and rigor of education. Let me go back and explain how hard was my adjustment at MIT. So, given the background of those rigorous studies and tough environment in high school that I was in, MIT was a piece of cake. I felt it was so easy- my college mates were kind of screaming and kicking and saying this is a tough place to do an undergrad. All the time you have to study! And for me it was, despite the fact that I had skipped last year, it was still easy compared to what I was used to in Alborz High School.

Zierler:

Cumrun, at MIT, was it a professor or a specific class that compelled you to focus more on physics?

Vafa:

When I first started MIT, I was interested in electrical engineering, and economics. Because I assumed that I am going to go back to Iran after I finish my education. There was never a thought that I'm going to stay in the U.S. So, I was saying, okay, I'm going to go back to Iran. Iran needs engineers, needs management, needs somebody who's familiar with these. So, to me, a combination of engineering and management/economics sounded a good, attractive option. So, I was thinking of double majoring in electrical engineering and economics when I first went to MIT. And the first term I took courses which were a combination of those. I took courses on microeconomics and in electrical engineering. The course on electrical engineering, I remember it was on electric network theory. I also took courses in physics and math, which went along with anybody at MIT: Everyone would take math, calculus, and physics. I liked doing courses in computers, which was at that time on the IBM punch-cards. I remember having fun with computers as well, and so I was kind of trying to learn those. But as far as the courses I wanted to major in, I didn't like the sophistication of the topics discussed in courses. I didn't find economics that compelling. Mathematically, I felt that each time they were trying to talk about the slope of some function, they would say the marginal rate of this or the marginal rate of that. And I was saying, I was a bit frustrated with why don't they talk about slope of demand curve and supply curve instead of marginal rate of this, marginal rate of that? I also found it a bit morally unsatisfactory, and this was nucleated for me at one point. In my economics class we had the assignment as to what economic policy we could implement to dismantle or to cause trouble for OPEC? Now, OPEC at that time had become a powerful entity in terms of oil and prices of oils and so on. Perhaps for my teacher, as an economist, it was natural to ask such a question, but for me coming from Iran, where OPEC and the oil revenue has really translated to a big advancement of the country toward becoming more advanced, it was a very strange kind of question. I wondered where is the morality of what they are teaching here? And so, I found this very immoral, and I told my teacher I'm not going to do this assignment. And he said why? And I said, well I don't believe in this thing that you are suggesting. He said, "No, no, no, I'm not saying you should do it, I'm just saying- I'm just wanting you to practice what kind of economic policy would do what." I said, "No, I'm not doing it. I'm not interested in doing this assignment, I won't do it." So, it was kind of a moral statement. I found economic policies can have immoral implications and I was very disappointed in that. So that was one course. And then engineering, electrical engineering, so we were learning about networks and resistors, capacitors, inductors and all that. And how you solve the current in the circuit and so on. They give us certain rules of how you compute things. In this circuit, you do this and that, and then this thing, okay, but can you explain why these rules work, or where they come from? And the teacher, professor, would say, "No, you don't need to know the reasons behind the formulas to solve for the currents and voltages in the circuit. You just need these rules." I said, "But I want to know where you got these rules from." He said, "No, that's not the point of this course. The course is to try to teach how you compute these are the rules you use (laughter). I'm not interested in teaching you where they come from. That's not the main point of the lesson."

Zierler:

You were interested in something more fundamental.

Vafa:

More fundamental. Where is it coming from? Where are you getting this from? And so on. So, this to me sounded like a recipe book more than something that I wanted to attach a deep meaning to. So, I found it very frustrating. So, neither that engineering course, nor the economics course attracted me.

Zierler:

Cumrun, you're still wondering how the moon doesn't fall from the sky.

Vafa:

Well, I had by that time learned it in my classical mechanics course.

Zierler:

Okay (laughter).

Vafa:

But still, I found it interesting of course and really pleasant. And physics was very easy and came naturally to me. And then I took a second course in my first year at MIT, and I'm going semester by semester because that's crucial about how I changed my view. I took a course on electricity of magnetism for my second semester in first year, when I was a freshman at MIT. It was a course on electromagnetism based on the book by Purcell. That book by Purcell on E&M is in my opinion one of the fantastic masterpieces of education in physics. Especially for basic physics. And it really attracted me to physics. In that book, he kind of uses intuition but geometric intuition, mathematical intuition, to try to impart physical laws of electricity and magnetism, which I always found a little bit abstract. I remember, I forgot to say perhaps that towards the end of high school, I was really trying to learn electricity and magnetism on my own from an English text. And I was really baffled by the notion of fields. What does it mean to say electric fields, like an invisible thing there, and so on. So, it kind of was very mysterious. And then through this course by the second semester at MIT under teaching from Purcell's book, I was amazingly attracted to the whole subject. And I was really enchanted by it. And so, at the end of the first year at MIT, I was kind of puzzled. I was finding both mathematics that I was learning, calculus and all that, attractive, and also physics was very attractive. But neither economics nor engineering seemed attractive to me. And so, what was I about to do? In second year, we were supposed to declare our concentration or major at MIT. First year there is no requirement for declaring, but second year we were supposed to declare. I was confused what to do. So that summer, I went back to Iran to visit my family, and I told my parents, this is what it is. I'm not finding engineering and economics very satisfactory, but I'm finding math and physics very attractive to me. But I didn't think that math and physics would be an attractive thing as a job in Iran. So, if I were to study math and physics, I felt at that time, the highest ambition you can have if you were to live in Iran is to become a high school teacher or something like that. And that didn't sound very ambitious to me as a job option. So, I was kind of puzzled, confused I would say, about what to do. My parents never tried to push me one way or another as to what to concentrate on. So, at that time, I think my father said, "Well, let's go and talk with some of our friends, see what they think about it." He had a friend, Dr. Niazmand, who was educated in the U.S. but was also one of the prominent industrialists in Iran. You know, patriotic and kind of a figure who was both interested in Iran and interested in applying what he had learned about management and engineering to the actual problems of the country. So he said, "Well, let's go and see what he thinks about this" I went and talked with him and I explained to him exactly what I told you about my interests, and what I did not seem to be that interested in, to see what he thinks? He said, "Well, if you're interested in math and physics, study math and physics." I said, "Well, but if I study math and physics, then I won't be able to necessarily find a good job in Iran. That would not be very attractive in terms of a job." He said, "Well, so don't come back to Iran." I said, "What do you mean, don't come back to Iran? I mean, I'm interested in coming back to Iran (laughter). What is..." So he basically was trying to tell me, just follow your interests regardless of whatever happens and I found it very surprising by somebody who was such a patriot doing all these amazing things in Iran, but still he's telling me, you know, follow your interests."

Zierler:

And again, Cumrun, at this point, the brewing political crisis, the Revolution, this is not part of the decision making?

Vafa:

No, [the] Revolution did not impact my decision. Unrest had just begun to happen that summer. Actually just a few months before that, there were some uprisings in Tabriz, in the wintertime if I remember correctly. So, when I was first year at MIT, I had begun to hear things. And by the summer, when I was in Iran, things were beginning to boil and that's where they had the event of the killings in a cinema, the burning of a cinema that people on the one side were saying government was doing it, the government was saying the instigators were doing it. So, it was becoming a bit more chaotic. But still, no. I wouldn't say there was any worry about, at least not from my perspective, about any change or any assumption that anything is going to be changed politically. So, this did not impact my decision. I was a bit confused about what to do. But after this discussion with Dr. Niazmand, I was more reinforced to follow math and physics and not to worry right now about the future or eventuality. So, I decided to postpone my decision about where I'm going to go and what else, to later, but just follow my interests. And so, when I came back to MIT for my sophomore year, I went and took a course of math and physics as concentration. So that's the decision process. But as far as the math, I should say I was greatly impacted by my mentor there, Prof. Daniel Quillen, who was my calculus instructor in my first course in freshman year. Daniel Quillen was an amazing mathematician, and he had already won the Fields Medal, but he was teaching just the elementary, basic calculus course to us. I really loved the way he was teaching it to us and so I got to talk with him after the class about other topics in math on some more advanced topics. And he became my advisor second year as soon as I declared math as [my] concentration. I asked him to become my advisor and he agreed. And so, I had kind of a very good mentor, I would say, during my MIT years, in terms of what to study in math. And also, later on I got also a good advisor in physics, Prof. Roscoe Giles, who also helped me with the orientation with what to do in physics. So, I was kind of benefitting from both sides. Mathematically, Daniel Quillen was telling me about [the] importance of topology and mathematical ideas in modern physics. He imparted on me the importance of learning some of these new ideas that are coming to impact modern physics at that time. One of them was called instantons which they had just discovered a few years earlier. So, it was something that Daniel Quillen was of course aware of, and he was trying to tell me it's a kind of physics that I should learn and its math underpinnings and so on. He encouraged me to study the lectures of Sidney Coleman on that subject which was just a year or so old. So, I was driven in that direction of learning more math, which is useful for physics. And so, I found this potential interest in combining math and physics very attractive, and that someone, at the mathematical caliber of Daniel Quillen himself being interested in physics and advising me was a very lucky thing for me.

Zierler:

Cumrun, was anybody talking about string theory in its earliest form that you can remember as an undergraduate?

Vafa:

No. No.

Zierler:

So names like Veneziano, Green, John Schwarz, you were not aware of any of this?

Vafa:

No, I had not heard any of those names. I think, I mean I had heard about some of the big names, for example Feynman and his lectures. I had seen films of his Cornell lectures. I had seen some of those, and so I was really amazed by him. But no, nothing about string theory. The only other thing was that perhaps in retrospect, is interesting to mention is that MIT had initiated a program called IAP, Independent Activities Period, where during the month of January, when it was a recess between the fall and the spring term, they would have this one month of basically free learning. Everybody can do whatever, and professors and others would put mini courses, like one-hour lectures or two-hour lectures, or something on some topic of their interest. And I remember one of the topics I went to listen was a talk about gravitational waves by Rai Weiss. And that was one of these one-hour lectures. I went there with ten other people maybe, and here there was this guy who was telling us, you know, there are these gravity waves and so on, and we're going to detect it soon, and so on, which I knew nothing about. It sounded very dreamy. Perhaps because I had not yet studied general relativity it sounded not real to me. It sounded like, hmm, that's interesting, but no, it didn't sound very real to me. But in retrospect, I thought I should share that recollection of that lecture at IAP. It didn't make huge impact on me at that time, but historically it was kind of an amazing lecture I saw. The beginning of an effort which led to the detection of gravity waves four decades later!

Zierler:

Cumrun, was anybody teaching general relativity at MIT when you were there as an undergrad?

Vafa:

They were, but I never took any courses on general relativity. Neither in college nor after that. The reason was this: when I was in second year, at MIT, I was talking with my advisor, Daniel Quillen, about which courses I should take in math, and he was telling me, you know, you should take whatever courses, but you can take this, differential geometry, or topology or algebra or- and I said, okay, so what should I take? He said, "Well, okay, differential geometry does this, topology does this, algebra does this…” And so, I said, "Okay, so what should I take?" And he would repeat the same things. So, in the system I had grown up in Iran the courses are fixed for you. You don't decide what course you take. You are given the material, the book, and all that. It's decided for all the students in the whole country and they tell you. And so, this is the book you study. And more broadly the system I had gotten accustomed to was to identify some person I trusted in terms of his knowledge and ask that person’s advice as to what I should study. And so that was, in this case, Daniel Quillen. I had decided he knows the stuff really well. And so, I insisted again to decide for me, and he would not give me the exact course I should take. So, he was kind of again going over the list: A, B, C, D. You decide what you want to do. One of the other things that I learned from him was this: I said, "Okay, what would you do?" And he said, "Well, you know, the way I would do things where, you know, I would skip a few courses. I would study something on my own, I'd skip one course and take the next course, which was hard, but then I would read some course back, and I'd jump a few courses and so on. So, I quickly go from one course to the two courses up, not the next course up. So, it's up to you what you want to do, but that's the way I did it. So that's the way I studied." I said, "Okay, I'm going to take differential geometry, graduate course." In my junior year at MIT. Third year at MIT, not enough background, trying to follow how Daniel Quillen does it. Differential geometry. I was miserable in that class. I did not have the background, I was with other graduate students, and it was one of the worst experiences in terms of my courses that I took. Unlike the first year of MIT, which everything was nice and easy and smooth. This, on the third year I was doing this ambitious thing, trying to get the graduate course in differential geometry, and I was so completely miserable. With inadequate backgrounds, I was not getting the motivation of the concepts. It was too advanced for my understanding. But anyhow, I struggled through it, you know, really spent hours and hours trying to learn about this, and eventually I learned it. But it wasn't with pleasure. It was really painful. Painful learning. But I would say at the end, I kind of understood what differential geometry was. And then I was opening up books on general relativity. Big book like Misner, Thorne, and Wheeler, “Gravitation” and so on, and I would say, "Okay, I know differential geometry now. Okay, what's the Einstein equation? Curvature tensor related to stress tensor? Okay, okay fine, I understand it." I'd just do a few examples. "It's okay, I don't need to take a course on this" (laughter). So differential geometry replaced my course in general relativity, which is probably a mistake I did, but at any rate, at that point I felt that I knew enough about general relativity from the "sources" that is from the mathematicians. Kind of know what the subject is. Not from physicists, who may not know exactly what differential geometry is. So, I felt like I have a deeper understanding, just because I knew the math better. Which is not correct, but that was my conception of what the general relativity I needed to know, and I studied on my own. So, I didn't take- I never took general relativity.

Zierler:

Cumrun, at what point in Iran did the situation get so bad that you knew you couldn't return home or perhaps you were even worried about your family's safety?

Vafa:

No, I was never worried about my family or my not returning in Iran. I mean, to me, the family- first of all, my father was in Belgium when the revolution happened. Even though if he were in Iran at the time, there could have been a bit of a problem because he was higher up in the government. But the fact that he was not in Iran didn't give me any worries about what might happen to him. And I was not worrying about not ever going back to Iran. To me, that was not an option regardless of what happens to Iran. So, to me, that was not an option. The revolution was happening the second year when I was at MIT, and I had been going back and I continue to go back to Iran now, and so did my father. So, I don't think that affected us in terms of our connection to the country. So, I've always tried to keep politics out of my interests in Iran. Iran is for me a broader concept. It is a concept of people, and the culture, and so forth. And that I have never decreased my interest in since I was a child. That has not changed.

Zierler:

Cumrun, that's an observation from you looking outward. Of course, during this time, this is a very dark period in American-Iran relations.

Vafa:

Yes.

Zierler:

Did you ever experience during these years in Boston, any anti-Persian sentiment?

Vafa:

Well kind of, a little bit. Nothing like physical or such things, but during the third year I was at MIT, it was the hostage crisis.

Zierler:

'79.

Vafa:

I had very good relations with my MIT fellows, the students, but you know, there was for some of them, the fact that I was from Iran and so there was a little bit tickling them occasionally. I never felt any animosity specifically towards me. But on our dorm, I was in a dormitory at MIT, MacGregor House. They would put banners, some of the students, on their windows saying, "Nuke Iran." Okay, that I didn't find pleasant. So that kind of thing, it was indirect. So, it wasn't personal, but it was kind of in your face, you could see it. So it wasn't that pleasant. And a few remarks here and there, which was kind of, "Oh yeah, you're from Iran," or something. But nothing really that much. I think I was kind of in a shelter in the sense that MIT was much more tolerant and understanding of this kind of thing. They were much more understanding of the situation than at other places in the U.S. For example, I think at the same time my brother who was studying in the U.S. had more difficulty with his passport or something like that. He had to go to renew it as all Iranians had been made to do. The Carter government was giving trouble to Iranian students in America also due to this situation. All the students who were on some kind of scholarship were not going to get scholarships because the funds were disconnected and all that. So, there was a bad environment for this situation between Iran and the U.S. And I think the problem was that Carter and his administration was misfiring towards the wrong direction. For example, Iranian students and Iranian who were studying in the U.S. It was incorrect policy. But I think I was sheltered. I was sheltered in the sense that I didn't feel [a] direct threat of any kind. So, I kind of ignored it more or less. I continued my studies without worrying about it.

Zierler:

Cumrun, as you emphasize, you felt free to go back to Iran. You didn't think that you would stay in the United States forever. As you were considering graduate school, was that a factor at all? Did you know at least for the short term that you wanted to stay in the United States?

Vafa:

I think that more or less when I decided to do math and physics, I had half-thought that that might be the eventuality anyhow. Had nothing to do with politics at that time. There was no inkling of that. And so, the decision I made was based on what I was interested in. And so, I think that it was a wise decision to follow my interests, and I think I owe it to our friend who was giving that advice. Not to worry about whatever eventuality might be, just follow your interests. And that has been the advice I have been giving to anybody who asks me about what they should do in terms of their studies.

Zierler:

Did you consider math programs as well, or you knew you wanted to do a physics PhD?

Vafa:

That's a good question. So again, towards the end of my studies at MIT I was doing some soul-searching. At the end of my third year, beginning of fourth year, it was at a time at MIT that I had to apply to graduate school. And I had to decide exactly that question, what am I going to be doing? Math or physics? And math was always easier for me to study, and reading math was much easier. For example, a math textbook I could do it on my own very easily. Well-stated, well-formulated, everything was clear. Physics was sometimes a little wishy-washy to me in some places. Like you know, yeah you should feel it this way, you should think of it that way and so on, it was a little bit like kind of a little bit of feeling involved, right? Sometimes not very precise. It appeared to me a little bit like that. So, I was a little bit frustrated with that part of physics. On the other hand, math, even though it was very beautiful and simple and all that, there were pieces which didn't attract me. For example, I remember learning different principles in topology, and the axiom of choice and this and that, that they said, "Okay, you know, we want to prove this theorem where if you want to prove this theorem without this possible assumption, then you can find the counter-example." So, they said, “Show there is a counterexample if you relax this assumption." And to do that, you had to construct a counterexample involving a construction of infinite set of doing this and that. It seemed nothing to do with reality to me. Sounded like, okay, you can prove it and there's this condition needed, but what? So what? It didn't excite me. It wasn't like, okay, this is- finally I now know what math is. No, it was kind of like, there's this technical thing. Yeah, you can do this infinite construction of some set as a counterexample to that theorem, if you didn't have this condition, but so what? In the grand scheme of things, it was a waste of my time, I felt. By spending all this time to try to find a counterexample. Just pinpoint this little condition that I really need. To me, that was not as exciting. Physics was the guts of what's going on. It was exciting, what's going on in the Universe! On the other hand, it didn't have this flavor of the rigor that I wanted, as much as the math had. So, I was kind of a little bit confused about whether I am going in the direction of more math or more physics, as I had to make a decision. And so that was a confusion I had. And I ultimately found that physics is what I'm really interested in, despite the fact that I felt it was harder for me, to make it intuitive for me. So, to make physics intuitive for me was always more difficult compared to math which came easier. But I felt I have to do this, because this is really what I'm interested in. Math, perhaps, I could be better at, but I wasn't as excited about it as in physics. So, I decided to go after what I'm excited about and [I] applied to physics graduate programs only.

Zierler:

It sounds, of course, just to foreshadow, you would be the perfect graduate student to Ed Witten, who's recognized for his mathematical abilities, even though he's a physicist.

Vafa:

Well that perhaps was not totally accidental. You see, when I was applying to graduate schools, I was talking with people where should I apply to? And they were telling me different places, but one of the places I heard from a number of people, including from my advisor, Roscoe Giles that in Princeton, there is this amazing rising star, Edward Witten. At that time, he was only a few years after his PhD. He was already well-known among theoretical physicists! So, I felt that's the kind of a place/advisor that you might want to consider if you want to apply for graduate school. So, I applied to five or so places and I got admitted to all of them, including Harvard, Princeton and a few more places. But Princeton stood out, and I felt that would be a great place to work with this rising star, Edward Witten. And so, I had that in my mind. So, when I decided to go to Princeton, that was on my radar from the beginning.

Zierler:

Now Ed, he was in the department at that point, or he was at the Institute?

Vafa:

He was at the department. So, then I went to Princeton for graduate school without hesitation. During the first year in graduate school, I was still kind of torn between the math and the physics interaction. I felt that the math/physics tension hadn't resolved in me, so what am I doing here? The physics is not rigorous- I'd learned a course on quantum field theory while at MIT. Actually, from both Bob Jaffe at MIT and also a legendary course by Sidney Coleman. When I was at MIT, there was this option of cross-registering and taking a course at Harvard. And so, while I was a senior at MIT, I took two courses at Harvard. One was a course by Sidney Coleman on quantum field theory, and one was a course by Raoul Bott on differential geometry. So, I repeated differential geometry by taking Raoul Bott's course. Both were amazing courses, and I really enjoyed the course by Raoul on differential geometry. Now, after I had seen it once, I had more of an understanding and a more intuitive feeling of what differential geometry is rather than technical issues. So, I really liked his style of teaching. And Sidney Coleman, you know, he's a legendary lecturer and legendary teacher, legendary physicist. And he was already famous, his quantum field theory course was famous, so taking that course for me was an amazing thing. But as I was learning it, I was again frustrated by the fact that the way you do the calculation in quantum field theory, you find this result which is infinite, and you do this trick and you make it finite and move on. And this was called renormalization. And to me that operation was ugly. And-

Zierler:

What was ugly about it, Cumrun? What do you mean?

Vafa:

Well, the answer came out to be infinite, so anybody who wasn't cheating would say the answer was infinite. And then you want to get a finite number out of it, and you say, "Well, we do this thing and we do that thing, and we get a finite number if you do it this way." I said, that's a cheat, that's a trick. That doesn’t make sense- does it really exist? What are you guys doing? And so, on and so on. So that was part of my frustration. When I mentioned that when I was an undergraduate and trying to decide what to pursue, these were kind of part of my frustrations. And so, this frustration about the lack of rigor in physics, did not resolve itself in the undergraduate years. So when I went to graduate school, when I was starting the graduate courses at Princeton, I said, okay, I'm going to take quantum field theory from the physicists, a great course by David Gross, but also I'm going to study on my own, axiomatic quantum field theory text by Bogoliubov I think, or similar texts. I'm going to study that, and I'm going to really learn what quantum field theory is at the same time as I'm going to learn it from the traditional course. And so, David Gross's course would start and go quickly from topic to topic to topic, and I was still on chapter one in axiomatic quantum field theory textbook. I'm barely learning what's going on from the axiomatic approach. So even the course was proceeding, and my attempt at a rigorous understanding was going nowhere. So, I felt, look, this is not working. I mean, this axiomatic "quantum field theory," that approach that I'm trying to understand, does not seem to be the right way to think about this topic. At least it's not very fruitful. So, I was kind of beginning to have a second thought: if you're going to stay in physics, if you're interested in learning physics, you have to think like how a physicist thinks about it. So, this was [the] beginning to evolve my way of thinking about physics. The thought that rigorous math should not be a prerequisite, but a physical understanding, a deeper intuitive understanding instead should be a requisite. But I still had not found what does it mean to have a rigorous physics understanding. What does it mean to build a physics intuition? And why is physical intuition not as wishy-washy as I had thought? How do you think about physics to make it not the wishy-washy thing I had felt, but a very robust subject? That took a while for me to figure out.

Zierler:

So as you're saying, Cumrun, the wishy-washiness is really more a product of your lack of intellectual maturity in this field?

Vafa:

Correct, correct.

Zierler:

That it's actually not wishy-washy, it just took some wisdom on your part to understand that.

Vafa:

That's right. As this first-year graduate student at Princeton, I still felt it was wishy-washy. So, I had not matured enough to appreciate a different view of physics. And so, in my view math was still supreme and physics was kind of trying to aspire to it. It wasn't quite catching up. But there was exciting stuff in physics, because it's reality. That was kind of my perspective at that time.

Zierler:

You're for sure aware of the famous Richard Feynman quote, right? About the difference between math and physics?

Vafa:

Which one of it do you have in mind?

Zierler:

I almost would blush saying it, but it's the one where physics is the real deal (laughter).

Vafa:

Oh yeah, yeah, yeah, I know which one you're talking about.

Zierler:

When did you first connect with Ed?

Vafa:

I think second year. In second year, after I took my basic courses, I think. I think it was second year at Princeton, if I'm not mistaken. And-

Zierler:

And it was a course that you took? It was a lecture you attended?

Vafa:

No, I just went to his office. I said, I want to work with you. Do you have anything I can work on? And he gave me a few of his papers I should read.

Zierler:

And what was he working on at that point?

Vafa:

I think one paper he gave me to read was a paper he had written on Kaluza–Klein theory and Grand Unification. Predictions of the fine-structured constant or relation to fine-structured constant and Kaluza–Klein compactification. And a few other papers. I don't remember the details right now. He also told me his plan was to study string theory. He told me he was trying to learn string theory. He said, "I don't know about string theory, but I'm planning to learn it." And I said, "Oh, okay. I'll be interested in learning it too. What is a good paper to learn it?" And he said, "Well, there are these review- there's a review article that just came out," I think it was in the form of a Physics Reports by Green and Schwarz. So, I said, I will study this and see what I can do. So, I remember trying to learn string theory. This is my second year at Princeton. And I looked at this review article by Green and Schwarz. And it sounded to me like it was too ambitious, trying to do quantum gravity and everything about this and that. I saw nice pictures, you know, of spheres, holes, torus, and so on. I said, "Wow, this is cool." But then I got to the thing, it seemed to be confusing: they seemed to be talking about two-dimensional quantum field theory. And you know, not only that, the free field theory in two dimensions. How could a boring 2-D free theory describe quantum gravity? It wasn't quite clicking with me. And then worse than that, it was going to the light cone. The description broke Lorentz invariance naively as they had to go to the light cone gauge. And so, everything was kind of strange to me. One couldn't do it in a Lorentz invariant way, you had to go to light cone, and then you're only talking about 2-D. And somehow that 2-D theory is going to transpire to give you quantum gravity in the extra dimension, and the dimensions were not even four but rather ten! What is going on? And I said, look, okay, I said this might be interesting, but it doesn't seem to be mainstream physics. And so, if I do this stuff, and if I want to become a physicist, and I just did this stuff, nobody is going to take me seriously. This sounded a little bit of an exotic kind of thing. So, I told Witten that, yeah, I would like to do work on something a bit more mainstream. I didn't want to work on string theory. So that was my-

Zierler:

And Cumrun, just to zoom out for a second, this is all happening before the so-called superstring revolution that gets started in '84?

Vafa:

This is 1982 I'm talking about.

Zierler:

Yeah, yeah.

Vafa:

So that was before then. Two years before then, and I said, look, I'm just trying to learn physics and I don't want to do things which are not going to mainstream. And this string theory thing looks a bit risky, you know.

Zierler:

Maybe even a little wishy-washy, as you say.

Vafa:

Wishy-washy. It wasn't clicking. It wasn't clicking. You know it's two dimensional- I didn't get it. I didn't get it.

Zierler:

What was compelling about this to Ed though? If he shared with you that he wanted to start working on this?

Vafa:

He didn't tell me why he was interested. He just told me that's what he was going to study and learn. My encounters with him, especially at the beginning, were very brief. He was very telegraphic and he was kind of like, "Go on, do it yourself." kind of, ``I'm going to be studying this, if you also want to do this go on and read it and come back”. In fact, originally part of the thing was we didn't click very well, with Ed. At some point, one of the discussions I had, I went to his office and tried to review what I had learned. And he says, "Don't tell me what you have learned. Just tell me what's new.” I was disappointed with that. So, I kind of said, okay, that's that. I'm not going to have Ed as my advisor. So, I decided that's that. So, I went and started working with Stephen Adler in the Institute for Advanced Study. I tried to discuss some topics with him about quantum field theory. So that was my original interaction with Ed, and it didn't go that well.

Zierler:

What were you working on with Adler? What was he doing?

Vafa:

At that time, I had been interested in quantum field theories, and I was trying to do things that were related to symmetry breakings. And I was I think- I was really trying to understand why in QCD chiral symmetries get broken. That's what we were trying to do. I was learning the topic and so on and reading review articles on that, I think one by Peskin. And so, Princeton had these coffee and tea hours, I think around four pm. And so, a few months after I had not talked with Witten about anything, I saw him there and he asked me, "What are you doing?" And I told him what I am doing. I said, "I'm trying to show chiral symmetry breaking." He said, "Well, that's too difficult a topic. Why don't you try to prove vector-like symmetries are not broken?" So, he redirected me to a different problem. So, we started talking about that, and then we noticed while talking that we can actually have a path to actually showing it. Just on the blackboard there were the things that began the discussion about trying to prove that vector-like symmetries cannot be broken, and then that started my going back to having Ed as my advisor. And that led to my first paper on that, proving that vector-like symmetries are not broken in QCD.

Zierler:

To come back to this theme of intellectual maturity where things start to click, what was it about this time that led to this first successful paper?

Vafa:

What led to it? I think the idea was simple and this was just a novel idea to try to use quantum field theory path integral, taking that seriously more than just perturbation theory. So, a lot of techniques people were using before were perturbative, and these non-perturbative techniques were beginning to take hold. So, trying to take seriously that quantum field theory is really the path integral. And properties of path integrals, structural properties, general properties of path integrals could already tell you about symmetries, and what can or cannot be broken was the basic input. That you don't need to get to all the details about the theory. Some general properties can already prove to you, give you some basic facts. And that was why I found that appealing, and we didn't have to do too hard! It was relatively, in some sense, straightforward, to prove it once you go to the basic aspects of quantum field theory, what it means.

Zierler:

And was this useful in terms of, on an inter-personal level communicating more effectively with Ed so that you could be a good graduate student?

Vafa:

Yes, yes, so I began a more fruitful interaction there. Understanding his style, and also what it is that, you know, he thinks how he thinks about physics. And I began to learn, actually from him, some of these conundrums that I had about the relation between physics and math. And so I mean, I already knew he was very good at math, but the way he thought about Feynman diagrams was not this formal technique of calculating perturbation series, but actually, you know, electron going there, photon doing that, and so on. So, internalizing that, that you should think about it as an actual particle doing it and not just the formalism. I began getting it and internalizing physical concepts in me, rather than viewing them as a formalism that one can derive. So by seeing him in practice doing actual physics, it imparted in me how one can think about physics, and how one builds physical intuition and how that can fit with math, rather than as a confrontation with math, the way I had found them; math and physics reinforcing each other. And that math and physics were not in conflict but actually in harmony, and can be used to reinforce each other; this came to reality while working with Ed.

Zierler:

And did that first paper directly feed into what would become your thesis research?

Vafa:

Yes. That was one of the papers I wrote. I wrote a few other topics on symmetry breaking and so on with Ed. One of them was more mathematical, which was published in Communications in Mathematical Physics, about the properties of eigenvalues of the Dirac operator. And the other ones, one other one was trying to prove that parity cannot be broken in the QCD, or vector-like theories and things like that. So, we did a few projects, a few of these topics. Through these projects, I also learned a little bit, a few philosophical lessons by interacting with Witten. Like when I was trying to work on a problem, when it was difficult, I would usually try to simplify it by going to a simple example, but then I would see that he was doing the opposite. He would say, "Well, let's ask a more general question." And to me, that sounded like what? We haven't even figured out this simple case, why do you make it a bigger problem? Don’t you want to make it a smaller problem? And by seeing him a few times doing this trick of taking a small problem and viewing it as part of a bigger problem, and then the perspective of a bigger problem solved the first problem, was wow. So, I learned a few of these kinds of insights from interacting with him, that are quite valuable. I should perhaps also mention that while at Princeton I was trying to continue my links with my Persian heritage, and it was for this reason that I took a Persian poetry class in my third year there. It was in this class, taught by Jeremy Clinton, that I had the luck to meet my future wife, the fellow graduate student Afarin, also from Iran, who was getting a master’s degree in Electrical Engineering.

Zierler:

Cumrun, as you describe it, it sounds like your thesis research was sort of several papers that came together for the dissertation. What were some of the themes that united all of these different papers, in terms of the kind of physicist you wanted to be? The things that were most interesting to you?

Vafa:

I think all of these were kind of themed in that they were rigorous. They were precise and the assumptions were clean. And that fit with my interest in precise statements. I didn't like ideas and statements which are only based on intuition but did not get backed by very precise arguments.

Zierler:

And of course, they're very mathematical. I'm wondering, did you ever work with Elliot Lieb at all?

Vafa:

No. Well, we interacted with Lieb. In fact, in one of those projects, which I mentioned, which was published in CMP, where we proved certain inequalities for Dirac operator eigenvalues. As part of that project, we were talking with the Lieb about inequalities, because he was quite an expert about deriving inequalities in similar contexts, so we were trying to get this input about some of them. So, we interacted with him, but no, I didn't work with him.

Zierler:

Who was on your thesis committee?

Vafa:

Edward Witten of course, David Gross, and Larry Yaffe.

Zierler:

Anything memorable from the oral defense? Any questions that stand out in your memory?

Vafa:

I remember the questions, I do- well, actually I do think I do remember actually that I didn't do that well in my oral defense, because the defense was not only about my research topic but it also included general random questions about physics. So, the research topic was fine. But then it came to random questions, and I was not good in random questions. So, I vaguely remember David Gross asking about, suppose I have a flower here and I put it in this room, how long does it take for you to smell it? I said a minute or thirty seconds- he said, "Okay, can you derive it? How long does it take for you to smell it?" And then I started doing some back of the envelope kind of calculation on the black board and I kind of derived it. So, he was happy with that, I think. And then I think it was okay at least. But then there was another question about super-cooling, I think? Something like that. The concept that he was asking me about. And I didn't know much about it. And I remember vaguely reading something about it before, but it was this kind of thing I wasn't very familiar with. So, I wasn't exactly sure. And he was asking me something about it. I remember an out-of-body experience, in the sense that I was seeing I'm answering him, but not understanding how I'm answering him. I was writing something on the blackboard, looking at what I'm writing, not understanding why I'm writing it and I was about to erase it and David Gross saying, "That's correct." So, it was kind of like, okay. So, it was kind of that experience I remember still, because I felt I have this different component of my mind that knows what's going on, the other one doesn't understand it. So, it was kind of playing at the same time in front of me. It was kind of a strange event about that thesis defense that I remember. But it was not my best performance in physics, I would say.

Zierler:

I wonder, were you warned? Was it a Princeton tradition that the defense would not really be about your specific research?

Vafa:

I think that's the typical situation on all the defenses I know of, and that was the same way. So yeah, that was not surprising in that form.

Zierler:

Cumrun, after you defended, what opportunities were available to you? What was most compelling for postdoctoral positions?

Vafa:

So that happened before the defense, of course. So that was the last year at Princeton, you apply to different places. So, I should say, there was one point I didn't mention, which was related to my graduate work, which was probably amusing. So, this was in summer of 1984. So that is when Green and Schwarz had done their calculation of the anomaly cancellation, and I remember I was at my office, I had come back from a trip, from I think the summer school in Europe, in Italy. Had come back to my office in Princeton on the fourth floor, and Ed's office is on the third floor. And he rarely came to our floor, fourth floor, but here he was, coming and knocking at my door, and then saying, "Have you heard about the revolution?" And here I was, "Revolution? What? What revolution?" (laughter)

Zierler:

"There's another one?"

Vafa:

I said, "What revolution?" He said, "The SO(32) revolution." Okay, that was my first introduction to Green and Schwarz's work. SO(32) revolution. I said, "No, what is it?" He said, and he was completely sure, confident, that physics is not going to be the same after this. He said, "Physics is going to change forever because of this, and now everybody is going to work on this." And so basically, that was that clear to him from the very beginning. And the paper had come out maybe a week ago or something, so this was very kind of new and fresh. So that was my introduction to string theory, and that last year in Princeton, I worked on string theory all the time, basically. And we wrote this paper with Ed, one of the first papers I wrote on string theory was called, "Bosonic string algebras." We were trying to understand some connections between different strings, which ended up using fractional oscillators, which was later interpreted by us as twisted sectors of orbifold compactifications. This in particular was the basis of a paper we wrote after this one with Harvey and Dixon on orbifold compactifications. So, the Calabi–Yau compactifications had already come out, but they were too complicated, but these orbifold constructions we came up with were basically free oscillators. So, using these oscillators, you can actually construct the whole interactions of strings, at least at some special points of compactifications, and so I was very happy with it. And that was in the last year in graduate school. So, I was kind of in-between about whether I should put that in my thesis or not. But I decided not to do that. So, my thesis does not include my work on string theory, even though it was done that last year.

Zierler:

When you were considering postdoctoral appointments, were you specifically focused on who you might work with in string theory?

Vafa:

No, I was not focused. At that time string theory was not a subject that had places where people were working on it. String theorists comprised of Green and Schwarz and only a few other physicists. So, it wasn't like, based on that, I decided where to go. I was just going based on reputation of the physicists more broadly. I was nominated to Society of Fellows at Harvard by Witten. And I also applied to some postdoctoral positions, I think in Caltech, maybe Chicago, I don't remember. A few places. I don't think I applied to too many places. So, Society of Fellows I was interviewed, and Caltech. And I remember my first offer came from Caltech. John Preskill, I remember, giving me the offer from Caltech. It was very attractive, you know. It was a very good salary and all that in a great place with wonderful physicists. But at any rate, when I got the junior fellow offer from Society of Fellows at Harvard, I decided to go to that one, because, not only it was an honor to be a junior fellow, but also Harvard had fantastic physicists as well. I was also already familiar with the Boston area and I liked it. So finally, I decided after two turning downs of Harvard, for undergraduate and graduate admissions, I decided this is the time to go to Harvard. So, I went to Harvard for the Society of Fellows. And became a junior fellow there, and that was the beginning and I've been there ever since.

Zierler:

Cumrun, I have to ask. So, it's just this amazing moment in the history of physics, whereas you say, it's really just Schwarz and Green, right? There isn't this community, this sociology of string theory at this point. So, to just fast-forward to today, it's an enormous field, there's thousands of people working on it. Did you sense at the time that this was really a frontier? That there was so much to do and so much to contribute? Did you understand-

Vafa:

Yes, yes.

Zierler:

-at the time that it would become this major thing that it is now?

Vafa:

Yes. I had already a lot of respect for Witten already, so in my interactions with him, I had seen his insights, and I had also seen his amazing speed in thinking. So, he would take these object things and quickly understand what the consequences are. So, I wouldn't take lightly what he thought about physics and specifically his views on string theory. So that is how it started. And then I began to be excited myself about the beauty of the subject and try to contribute to it. So, by the time I finished graduate school, I think I had already a clear idea that string theory is an open and exciting field. Many, many things are going to come out of this. And so, I was at that point driven to continue basically forever working on string theory and I also was sure about that. I was sure that this field was a growing field, regardless of who's working on it, and of course by that time, a lot of people had started working on it, by the time I graduated from Princeton. There was already a course, a seminar course by David Gross on string theory in my last year at Princeton, just because people knew that this Green-Schwarz calculation was important, and everybody wanted to get to familiarize and do research on string theory. It was kind of a last-minute course and almost everybody was attending that course. It was kind of a fundamental paradigm shift, and everybody knew that string theory is it, for now and the foreseeable future.

Zierler:

Did you join a group at Harvard? Were there people that automatically, it would make sense for you to work with as a postdoc?

Vafa:

Well, I came to an environment which was not as hospitable for string theory, actually. So, I remember meeting Glashow, for example. Shelly Glashow. The famous physicist. I'd already seen him once, or twice maybe. I had seen him in one of these MIT lectures at IAP. He gave a beautiful lecture about physics and grand unification and all that. I really enjoyed his lecture. And so I had a very good impression of Shelly, and so when I saw him there, and he said, "Oh, where are you coming from?" and I said, "I'm coming from Princeton, and I am working on string theory." And he said, "Huh, we don't have the `Ayatollah’ here." Now, I don't know why he said that, whether he knew my background from Iran, or whether he was referring to Witten or what, I don't know. But anyhow, that was Shelley's response to me when I first got to Harvard. And I think a few months later, or maybe a few months before, I don't know when exactly, I'd heard this comment from Howard Georgi, that string theory is “recreational mathematics.” That was the phrase. So, these were the views of senior physicists at Harvard about string theory, and so the only person who was not hostile towards string theory was Sidney Coleman, I would say. But he was not doing string theory either. And he was always kind of saying, "Oh, but I'm not smart enough to do string theory." Or something like that. He was never against string theory, but even him, after like a year or two, I began hearing things like, "Oh, after all the talk I've attended on string theory, the only thing I've learned is how easy it is to draw a Riemann surface!” (Laughter) So these were the senior people that were there. Now, the younger people were different. So there, there were younger people whom I interacted quite a bit. Luis Álvarez-Gaumé, who was I think assistant professor then, or associate professor. And Paul Ginsberg was assistant professor then. And there were also two other junior fellows, Gregory Moore and Phillip Nelson. So, these were the people I was interacting mostly in terms of string theory. So, the environment was really good actually, despite the fact that senior people were not as enthusiastic, these young people were fully interested in it, and I had this great interaction with them, and things moved.

Zierler:

When did you first connect with Andy Strominger?

Vafa:

I think I met Andy Strominger when I was an undergraduate at MIT. I think maybe my last year as an undergraduate I met him. He was just starting his first year of graduate school at MIT. And then I remember seeing him again, meeting him again, at Princeton at the Institute for Advanced Study when it was my last year in Princeton. I think maybe he had just become a postdoc there. Maybe his first year or second year. He had written this paper on the compactifications of Calabi–Yau. And he was working on trying to compute some number of particle generations for some Calabi–Yau’s which had singularities. And so, I remember interacting with him because he had calculated the number of generations for this manifold which disagreed with the simpler orbifold method for that computation that I had done and so I explained to him what the issue was.

Zierler:

When you were in the Society of Fellows, was your sense that you were being groomed to join the faculty at Harvard? Was that part of it?

Vafa:

No, not at all. Harvard was well-known for not promoting physicists from within.

Zierler:

Right.

Vafa:

Even if you got a junior faculty position at Harvard, it was rare to get promoted to senior faculty.

Zierler:

But you knew that Georgi broke the mold?

Vafa:

Yes. So, there were counter-examples, of course, and so it was not for sure, but Harvard had the reputation that it only gets the best in the world. And so, they don't care if you're part of Harvard or not. There's no bias towards being at Harvard. So being a junior fellow at Harvard was not related to accepting or thinking about long term. I was not, and to be honest, I never thought at that point about where I'm going to end up in long term. I already knew that being a junior fellow is an honor. Ed Witten and many other prominent physicists had been a junior fellow. So, this seemed like it's a no-brainer. You just do whatever you want for three years. They give you a good company of junior fellows, they give you wonderful dinner, and three years of freedom of whatever you want to do, why not? Well, the salary was not that high, but still the environment was good (laughter).

Zierler:

Do you have a sense who on the faculty was championing your promotion to faculty?

Vafa:

I cannot be sure, but I think Sidney Coleman was pushing it, in my opinion. And I think at that point. I knew the climate at Harvard for getting a faculty appointment was not very conducive in my field. So, I was applying to other places too. I considered other places such as I think UChicago and University of Washington [both of which] had contacted me to see if I am interested. At Harvard I think I didn't even apply. They told me, if I am interested to be considered for a faculty appointment, and I said yes, I am interested. Actually, to be honest, I never remember asking anybody to write me a recommendation letter for junior faculty. So somehow it happened. So, these places contacted me, "Are you interested?" I think Chicago offered me associate professorship. University of Washington was offering me professorship or something like that. At any rate, they were tenured positions. Or one of them was tenured. I don't remember which one. Right after junior fellowship. And Harvard was going to offer me assistant professor. And I told Harvard that would not do it. If you're just offering me assistant professorship, I'm not going to come, because I'm already getting, you know, something which is equivalent to associate professor with tenure, so why would I do this? So, then they changed the offer to associate professorship.

Zierler:

But that's still not tenured at Harvard.

Vafa:

Then that's not still tenured. So, I told them, "This is still not tenured is it?" They said, "No, but we can promise you we'll do a quick review, within a couple years." So, I said okay. So, under the condition that in two years, they will decide. Because I knew the environment wasn't that great in terms of string theory support at Harvard. I said, "Okay, within two years, you have to make a decision, because then I don't want to drag it here." Because I didn't feel the environment was necessarily pro-string theory.

Zierler:

Was there anyone between you and Georgi that made this transition? I mean, what other assurance did you have that this was the-

Vafa:

No, no.

Zierler:

There was none?

Vafa:

No, just nothing. I mean, I was at that point, I felt that I would have other offers, if Harvard doesn't work out. I didn't feel like I'm boxing myself into anything. I liked the Boston area, I liked Harvard. So, two years, no problem, I liked the area. I liked the environment of people working there, so I would interact with them. But no, I didn't feel like I would lose anything. But actually, now that we are discussing this, I remember this. I'd just gotten an offer for associate professor from Harvard and I remember there was an interview by BBC of prominent theoretical physicists including Feynman, Glashow, Wilczek, and others, about string theory. And you know, everybody was saying something. You know, Feynman had made these funny kinds of statements. He said- I remember Feynman's statement saying, "When I was young, whenever somebody old would come and say, 'Don't do this, don't do that' because they always would reject the new ideas in physics, I would see how wrong they are, these older folks in physics. So, I promised myself when I was young," Feynman said, "that when I get old, I would not make that mistake. So, when I get old, I would not say bad things about new areas and then trash it and so on. But here I go. String theory is wrong!” So, he prefaced it and continued by saying this. So, this is classic Feynman. And then in that same interview, I think Glashow had been asked what do you think about string theory? And he was saying, "Oh, it's not physics, not this not that." And in part of his interview, he had said, "...I don't like string theory, whatever. And I have done my best to keep string theory out of Harvard, and I have succeeded." Now here I was, just offered associate professorship, I had agreed to it. And here is a prominent Nobel Prize laureate physicist, Harvard physicist Shelly Glashow pronouncing string theory is out of Harvard and he has succeeded. So, I go to his office-

Zierler:

I think the phrase, Cumrun, was he specifically said he was on a campaign to make the department string-free.

Vafa:

Something like that. We can look at the exact wording now. But any rate, I went to his office. And I went to his office and I said, "Shelly, what is this? You have done this interview-" He said, "What is it?" I said, "About your interview with BBC." He said, "What about it?" I said, "Well, you just told them about this thing about string theory, and I've just become faculty here, and what do you think the prospective students who want to do string theory, will they come to Harvard? No way. I mean that's not fair to me. I'm not going to be able to do good physics here." He said, "Why?" I said, "Well, you said I'm trying to keep string theory out of Harvard." He said, "Oh, no, no, no. That was just for BBC, don't worry about that” (laughter). He said, "Don't you worry about that. Oh no, don't worry, don't worry. It's okay. No, no, no, we of course like to have string theory. Don't worry." And then a few months later, the printed version of that interview came out, and I see him saying, "I've done my best to keep string theory out of Harvard, and I have not succeeded" (laughter). Succeeded had been turned to not succeeded. So it was okay (laughter). So anyhow, those were the things. But yet they gave me this associate professorship, and I think within two years, they had the review, and they reviewed it, and they gave me a full professorship I think at the age of twenty-nine. So, I felt quite privileged, you know, by the age of twenty-nine being a full faculty at Harvard. So that was great!

Zierler:

And Cumrun, at this time, as string theory is starting to develop and you become a full professor, what are some of the things that you start to take on and where is the field headed at this point?

Vafa:

Well, string theory was by and large the domain of many young people. Many people kind of my age and maybe a little older, but not very old people. There were few older physicists who were willing to switch their direction. And so those are by and large younger people. Either a few older people like Green and Schwarz, who were founders, but most of the rest of the people were younger people like myself. So, it was a very active area, people were writing papers, new ideas were coming. And things were becoming more and more mathematical.

Zierler:

Mmhmm, right.

Vafa:

So, beginning with string theory, you would see mathematical concepts like “differential forms” that appeared in a physics paper. The words never appeared before. So, people were becoming less shy about using math jargon in physics papers. Previously, if you wrote math jargon in physics papers, even if you knew it and even if other people knew that, they all knew it, it would be a bad sign because they would say that, well, this is just showing off your math or kind of like trying to divert attention from the guts of the physics towards math, and this kind of like a side show that you don't want. So basically, the people, even if they use that math, they would hide it under the form of a physics description so that there was no such hints. But in string theory, math took a life of its own within physics. And became a little bit more normal not to be shy about kind of coming out of the closet with your math interests. Math enthusiasts in physics became bolder: "Okay, you know what? This is what it is. I'm not going to be shy; I'm going to use the math as it is. If you don't know about it, you're going to read about it." Kind of like I want to use this, and this is useful for my understanding of string theory. Not that I want to show off or anything, but this is useful. So, people became a bit less and less shy. And so that was kind of a movement towards a bit more abstract area of theoretical physics. So high energy physics, which is more bent towards particle phenomenology and all that, became more and more abstract. More theoretical, more mathematical, and just as topological ideas had begun to take hold with the discovery of instantons and with monopoles, a few years earlier, with string theory it kind of nucleated that the whole thing is really important, and understanding mathematics is nothing to be ashamed about. In fact, you actually have to do it, as a kind of a prerequisite. And this was kind of my dream of combining physics and math or working in an area where both work together anyhow. So, it was heaven for me. It was kind of like, wow. I couldn't have had it better. It was kind of an area I wanted to be working on, and somehow, they had come together in the context of string theory, mathematics and physics were one field after all.

Zierler:

When did you start to work with Andy Strominger on black holes?

Vafa:

So, I think with Andy Strominger, let me try to recall. So, I think there was a- so we have jumped about this string theory revolution and all that. The second revolution. I don't know if- that's a period which I think precedes that, so maybe we should first go to that one, and then-

Zierler:

Okay, that's fine. I thought that was actually earlier than the second revolution. So, let's start with that.

Vafa:

The second revolution was the main thing. So, this was, this started actually, it's actually quite an interesting interaction. It's an interesting history which I would like to share with you. This was 1994. I was, in the spring of 1994, I spent my sabbatical leave at the Institute for Advanced Study. So, Ed Witten had invited me to come there for spending the sabbatical year there, and I was there.

Zierler:

And he had transferred to the Institute at that point?

Vafa:

At that time, he had already done that. Actually, I should say that, you mentioned whether Witten was at Princeton or the Institute when I came. Even when I was asking him to become my advisor, he warned me that there was a chance he may not be at the university in the following years. And he asked me to keep that confidential. In case he moved, and I may have to move. I said I had no problem with moving. So he warned me, but at that time, I didn't know why he was possibly considering moving, but he had told me, and then a year after I had left Princeton, he had gone to the Institute and I wasn't surprised that he had moved. But at any rate, so yes, he had moved to the Institute I think in '86 or something like that, if I'm not mistaken. So yeah, he invited me to visit the Institute for Advance Study in 1994 for my sabbatical. So, perhaps I should explain the environment at that time. Nathan Seiberg had already been doing some very interesting work in quantum field theories for supersymmetric theories. And he had discovered these nontrivial dualities that he had conjectured, what we call Seiberg dualities, in the context of supersymmetric theories, which related strong coupling to weak coupling in supersymmetry QCD. Which sounded really remarkable, and he was bold enough to make these non-trivial conjectures. And there were some consistency checks. That was really coming up, and it was quite exciting. Nothing similar had happened in string theory. Now, as far as N=4 supersymmetric theories there was a long-standing strong weak duality conjecture, actually an SL(2,Z) duality of Montonen-Olive conjecture, which is similar to these dualities that Seiberg was talking about. It was a very nice thing, for the N=4 case it was simpler, and in some ways it was nicer. But it was difficult to check it because it related the weaker to the strong coupling, and people didn't know how to check any of this. Ashoke Sen had just written a paper showing that for N=4 supersymmetric case, the Montonen-Olive duality would imply that you should have certain bound states of electric and magnetic states. So, he actually proved that these bound states, which are predicted by the duality are actually there, and he calculated it. And proved mathematically that this prediction of strong-weak duality for N=4 theories works rather non-trivially. So when I came to IAS, we began discussing with Witten what is interesting, and we were both interested in this topic. So, I said, I'm interested in understanding this duality in the N=4 case, and he had also mentioned that what Sen had found was also fascinating for him. And so, we gradually began to think about it. SL(2,Z) symmetry was familiar to me from the study of torus amplitudes in string theory and I was enamored by SL(2,Z). The modular transformations of a torus. So, I was familiar with this and now it was showing up here unexpectedly N=4 supersymmetric case. I was fascinated trying to use this in some kind of a project to try to actually check this symmetry in detail. So the SL(2,Z) symmetry in string theory gave familiar modular forms with beautiful properties and I was curious to see whether those objects also appear here in the N=4 gauge theory as well or not? Same symmetry, not in string theory but in Yang-Mills theory. How could it be? It is amazing. How could a field theory have stringy features I thought? I was wondering how this stringy symmetry could be there for a field theory of particles? So, we began talking with Ed about this and then we immediately realized that instantons for N = 4 Yang-Mills will be a power series in this variable q, which should form a power series, which should have these modular properties. So if SL(2,Z) conjecture was correct, then somehow you should be able to get these modular forms from doing instanton expansions for Yang-Mills theory. These "stringy objects" should somehow arise in Yang-Mills theory. So, we began thinking about how to check these statements, so the natural setup ended up studying topological field theory, a subject Witten had introduced a few years earlier. So, we said, okay, if you have topological theory, you could in principle actually do the computation. Also luckily, you take some particular manifolds, like K3 manifold, which I was very familiar with, and was the first orbifold example I had studied. One of these amazing manifolds. The topological theory on K3 and the original non-topological theory were the same. So, we began studying N=4 theory on K3 and some other manifolds and using what mathematicians had known about instantons for such spaces. We found that putting all that was known by mathematicians together, we got the series of modular forms expected from the SL(2,Z) duality symmetry! That was remarkable. But what was next happening was even more remarkable. The computation for Yang-Mills on K3 gave us the partition function for bosonic strings! Bosonic strings, in twenty-six dimensions, popped out from the computation of Yang-Mills theory on K3. I was shocked!

Zierler:

Cumrun, why do you say computation and not calculation?

Vafa:

For me, it's the English language-

Zierler:

So you're not necessarily saying that this, that computers are necessary to make these calculations?

Vafa:

No, no, not computers. Calculations, sorry.

Zierler:

Okay.

Vafa:

Computation is not computers. Let's say calculations. So out of K3 came out these partition functions of bosonic springs, and out of torus, the only other example that was possible to do without topological twisting, was torus. And for that you get superstring partition function in 10 dimensions! So here, we were talking about no gravity, just gauge theory, on K3 and T4, and we were getting a partition function of two theories we knew of, bosonic strings and super strings. Wow, why is that? So, I immediately began to think this must be related to dualities in string theory. So, I was saying, look. If this is true for Yang-Mills dualities, giving you such structure which is showing a bosonic string partition function and superstring partition function, it's got to be related to dualities. So, in four dimensions, there were these electric magnetic dualities, and then I had heard already a few years earlier some string theorists had contemplated electric-magnetic dualities in the context of string theory. But electric-magnetic duality for string theory was relating strings in ten dimensions to five branes. This is the angle of the electric-magnetic duality in string theory. So, I'd heard about this, so then I remember hearing about this, so I just said, look. This has got to be true also in string theory. So, I remember calling from the Institute for Advanced Study [to] Andy Strominger. Because I knew Andy had worked on these string/five-brane dualities. I said, "Andy, you have written this paper about electro-magnetic duality in string theory. We're getting this amazing structure with Witten that seems like bosonic string is popping out, and I'm trying to see if there is any implication for dualities in string theory." And Andy explained his thing, and I didn't see any particular connection with that. And indeed, later on I learned that that connection with electro-magnetic duality was not the right way of thinking about duality in string theory. Electric-magnetic duality in four dimensions is not the duality that generalized in ten dimensions, but a different duality in string theory. So, I was looking at the wrong duality in ten dimensions, so that would not work. But nevertheless, I was convinced that this was not an accident. So, I made a bet with Ed Witten on an ice cream, which he paid later on, that this is the beginning of a revolution in string theory (laughter). That this has something to do with string theory. It's not accidental. It has something to do with conformal theories and string theory. It's not just accidentally popping in. So, this was in 1994. And in that same time. And during the course of the same project, with Witten, the following thing happened: we had known already that heterotic string compactification on four torus, gives you a theory in six dimensions, which has the same low-energy spectrum as type II strings on K3 manifold. Two different string theories on two different manifolds give you the same low-energy physics. So, one of them had been studied by Seiberg, the one on K3, and heterotic on T4, everybody had studied it starting with the work of Narain. And I had noticed they are the same and I felt it cannot be accidental. So, I told Witten, I said, "You know what? It could be that these two theories are actually the same. That this string theory on this T4- heterotic on T4, might be exactly the same as type II on K3- an example of duality in string theory. Just like Yang-Mills has this duality. And he immediately pointed out that a particular problem with this picture, and the problem he pointed out was that the heterotic string theory you can get non-abelian gauge groups in six dimensions, but if this duality was true, in six dimensions, type II strings on K3, you don’t get non-abelian gauge groups, so therefore it cannot be true. This objection that he raised actually ended up being incorrect later on. Because as he later on himself pointed out a year later in his own paper, singularities of K3 are the place where you could potentially get non-abelian gauge groups. But at that time, it looked like a problem for this duality. So anyhow, I had made this "conjecture" that maybe these two theories are the same. This point was not mentioned in our paper with Witten. So, in 1994, we wrote this paper with Witten about the N=4 Yang-Mills, and if you look at that paper, we are hinting that these dualities might somehow show up in string theory somewhere. So that was the beginning of my conviction that string theory duality is there, and we just have to find it.

Zierler:

Cumrun, you're obviously on fire with Witten at the Institute. Did you ever think about leaving to join the Institute?

Vafa:

Well, Witten had asked me whether I would be interested to join IAS but I said no, because I by that time [with] my wife had already sons and well settled in our home in the Boston area and happy with the environment we were in.

Zierler:

And you were happy at Harvard? That was fine?

Vafa:

I was happy at Harvard, yes. So, Witten raised the possibility. I didn't have any formal offer. But he raised the possibility, and I just said I cannot at this point consider doing it.

Zierler:

And where is Rajesh Gopakumar in all of this?

Vafa:

Oh, I didn't meet him until later. 1997 or 8. I think. He was a student at the time.

Zierler:

I think he was at Princeton. He was working with David Gross.

Vafa:

I did not meet him there. He might have been there when I was at the Institute for Advanced Study, but I was not interacting much with the students.

Zierler:

So when did you start working with him substantively?

Vafa:

He came as a postdoc to Harvard. But before we get to that, I think should get back to the exciting activities around that time, so the excitement for me already began in '94. And then a year later, Witten wrote this paper. Actually, before Witten's paper, Hull and Townsend wrote this beautiful paper about dualities in string theory and suggesting that the elevent dimensional supergravity is important in this. And Witten took that in his beautiful paper and expanded to many different directions, and in fact, in his paper, making a very convincing case of the existence of dualities in string theory. By the way, in his paper, Witten mentioned the conjecture I had made for the heterotic/type II duality. He cites me as well as Hull and Townsend because they also mentioned this possibility in their paper. So indeed, a couple years after our ’94 bet about the existence of dualities in string theory, I had won the ice cream bet, and I got an ice cream from Ed in CERN!

Zierler:

What were you doing at CERN? Were you visiting the theory group?

Vafa:

I think there was a conference or something. I think '96 or '97, I don't remember.

Zierler:

So let's get back to Andy Strominger and black holes.

Vafa:

Yeah, so after this duality happened, people were beginning to write papers left and right. One of the first papers was a very nice paper by Andy Strominger about what's called conifold transition, what happens if you have a singularity in a Calabi-Yau, and how do you describe it in gauge theory? He suggested this signals the appearance of massless particles. So, it's something he did, and I began talking with him about that, and we began to work on a project. So, with him, Ferrara, Harvey and Kachru, we generalized the duality between heterotic and the superstrings, which was only on up to six dimensions, all the way down to four dimensions. So, namely heterotic on K3 cross T2 being equivalent to type II on a Calabi-Yau threefold. So, we wrote a paper on that and there was a duality. And so that duality had interesting ramifications and so on, and so we developed it. So, we began discussing it. So, he visited Harvard, and at that time, I'd already become a full faculty at Harvard like six years before. But I knew that Andy was interested in coming to Boston area, and in fact coming to Harvard. So, he told me that he was being considered at the Institute for Advanced Study for a possible appointment there. And I asked him if he was interested in Harvard. And he said, oh yeah, he's definitely interested very much in Harvard. And so, we began talking about that, and also about physics. And so, that was part of the continuation of our discussion, when he was visiting Harvard and we began talking about black holes.

Zierler:

What was so compelling about this research for you?

Vafa:

The black hole? I mean, that was the smoking gun of deep facts about quantum gravity, that nobody had connected to string theory, and everybody said, "Well, okay, if string theory is a theory of quantum gravity, one of these basic facts about black holes which is the Hawking entropy and thermodynamic properties of black holes, where do you get it from string theory? So, a lot of string theorists were beginning to ask how you can derive the black hole entropy from string theory. That became one of the basic questions. People felt that now that we have dualities, now that we have understood string dualities, now that we understand strong coupling phenomena in string theory, now that there is no mystery about that, in some sense we are beginning to understand it, can we understand this other mystery of black holes? So, we were trying to understand black holes, and in particular count its entropy. We had learned that branes are important for this. Strominger had already described one example of it for conifold, but later Polchinski came up with these D-branes, these extended objects, and the importance of D-branes became immediately clear. But these extended objects when they wrapped around the cycles of the internal manifold became like particles, and if they wrapped enough times, they become like very massive particles, and if they wrap more and more times around these internal dimensions, they become very, very heavy, i.e., black holes. So, you could describe black holes by these objects. So, we said we can think about black holes like these heavy, wrapped objects. Can we now translate the question about the entropy or degrees of freedom of this black hole, which we cannot see, by deciphering them in terms of the number of degrees of freedom of these things wrapped around these internal dimensions? That became a very sharp question, a mathematical question, I was happy to see. Because I liked the concrete and precise mathematical nature of the question. Moreover, I was always enamored by the notion of not just arbitrary black holes, but black holes which are BPS. BPS or more precisely, extremal. Extremal black holes were going nowhere, kind of they are like stationary or quasi-stationary. And in the context of supersymmetric theories, these supersymmetric extremal black holes were known in the context of BPS black holes. So, these BPS objects were nice objects in string theory. I'd already learned that BPS objects are actually calculable in string theory. I had already seen examples. like calculations we had done with Witten for N = 4 Yang-Mills. I'd already seen BPS examples in my work with Sergio Cecotti when I had worked on two-dimensional BPS states and counting of them. So, I'd already been attracted to the notion of counting these objects, plus they were rigorous. They were precisely definable objects. They were something you really can count. They're mathematically precise. There's no vagueness in what they mean. They have exactly calculable properties. So, then getting BPS black holes would lead to a setup where the entropy could be calculated. So, in that context, I began talking with Andy. So asked my question to him, that would become something along the lines of, "Do you know of any supersymmetric BPS black hole whose entropy is not zero?" And then he would be saying that, "Oh yes, these are tough ones to calculate the entropy of one." For example, he had said that these extremal ones, BPS extremal ones, people like Hawking had already written a paper about it that suggested that the entropy might actually be zero. But Andy said, "I think they are wrong. I think they have made a mistake or something." So, Andy was saying, no, I don't think they have done it correctly. That indeed, you should be able to get entropy from these extremal BPS black holes. I said, "Okay, so can we work out one of these examples and see which one is the example?" So, we started with four dimensional black holes and we didn't make much progress because the calculation on the string side was difficult. We didn't have enough techniques to count them. But then somehow, during the course of that, I noticed the calculation becomes easier for higher dimensions, so I asked, "How about five dimensional ones? What do we know about their entropy?” So, the black hole calculation was similar in terms of being a BPS object. But the string theory counting was easier, and so we went directly to five dimensions. And doing the five dimension, exactly the same object that had come up in my work with Witten, which was the N = 4 Yang-Mills on K3 showed up. That same object which was part of the bosonic string partition function was not accidental anymore. I had already written a paper about that a few months before this work with Andy. I'd already explained why this observation that bosonic string partition function and superstring came up is not accidental. I'd already explained that in a paper. And now I was going to use that in the set-up of this project with Andy to actually calculate some new things for these black hole, and I focused on the calculation of these degrees of freedom, which I had the background for and I knew how to do it, and Andy was doing the calculation on the general relativity side and finding what is the prediction for its entropy? So he would be telling me, "Okay, the entropy of black hole is predicted to be this," and I would say, "Well let me count it using the microstates of branes and then use the Cardy formula, to find the asymptotic formula of these bound states." And we were finding the charge powers matched between the GR and stringy prediction, but we were off by factors of two! And so, he would check his computation and I would check mine and finally they matched! And we said, "Okay, we agree. Let’s stop checking further and write the paper. No more checks!” (laughter) So we immediately published it. So that was how that worked.

Zierler:

And then where does Rajesh enter the scene?

Vafa:

Not yet. This is in '96.

Zierler:

Okay.

Vafa:

So, Rajesh came as a postdoc I think in '97, if I'm not mistaken. I don't remember when he exactly became a postdoc, but I think that my work with him was ’97-98. So, by that time, we had learned about the importance of Calabi-Yau, and the role topological strings played in their deeper understanding. was important. I have to talk about the mathematical work on what's called topological string theory. And earlier than that, topological field theory. So, Witten had already introduced these objects in the late 1980s. Even before the 1990s, before string theory revolution and so on. So, he was talking about properties of field theory which can be topological, which don't depend on the metric details, as much as typical quantum field theories do. And he had introduced the notion of topological string, which seemed to be very special for Calabi-Yau threefolds. And so for Calabi-Yau threefolds, which were interesting for string theory for other reasons, it turns out these were most interesting, and so I had written papers with my collaborators, Bershadsky and Cecotti and Ooguri in early nineties on topological strings, probably the longest paper at that time in high energy theory, which was around 150 pages. At that time, it was unheard of to write not a review paper, but a research paper on a topic this long. But anyhow, we had written a humongous paper on trying to explore topological string and its properties. And it was really giving us results that were remarkable, because it was counting the number of curves, the number of, you know. How many ways you can fit a surface with a fixed number of holes inside a Calabi-Yau, and mathematicians were having difficulties on how to do these calculations, and we had discovered these techniques using mirror symmetry, a topic I did not talk about, which is one of the things that I conjectured in my paper with Lerche and Warner. How they come out, and we used these techniques of mirror symmetry to try to calculate how they arise, how many they are, and so I was very enamored with that. In fact, when we first conjectured mirror symmetry the mathematical evidence was against it- there were more Calabi-Yau manifolds with negative sign of Euler characteristic known than positive, but mirror symmetry predicted they are the same. Nevertheless, we were bold enough to conjecture it which turned out eventually to be proven correct! Anyhow, so we had done this calculation for topological strings using mirror symmetry. But these calculations did not give you only integers, which naively expected if one is counting something. They would give you rational numbers. So somehow, with Rajesh we were trying to see whether or not you can extract from these, integers which count objects, like BPS of black holes, can you actually decipher integral numbers which count particles, out of these topological string calculations? And so, with Rajesh, we wrote a couple of papers understanding that better, as well as probably the large N duality that had come out in some of these theories when you had many topological D-branes.

Zierler:

And then where is F-theory in all of this?

Vafa:

I think we are going back and forth. So, F-theory work was very close to the time I wrote the black hole paper. I think maybe a month later or something. And so [the] F-theory paper was a duality, which led to a different perspective on what M-theory dualities are. That there’s just an eleven-dimensional theory, the M-theory, that you can get all these other theories by compactification is true but not quite the best viewpoint as it turned out. It turned out for example, type IIB in ten dimensions, you cannot get directly from M-theory. So, what you do, if you want to view it from M-theory, you go from 11 dimension down to nine dimensions, on a two torus, and then you shrink the size of the torus to zero size. So, if you shrink it, when you think you would be going from 11 to nine you actually end up in ten dimensions, the type IIB! So that had already been understood, but it was bizarre. So, it showed that M-theory is not understanding type IIB in ten dimensions in a natural way. So, there was in some sense a torus lurking around in ten dimensions for type IIB, which you could see via M-theory only if you go to nine dimensions. So, then I said, well, maybe we should think about this torus as something more real. That in ten dimension, there's two more dimensions. And so then you can use this to construct new compactification of string theory by playing around with how this torus varies over the space and all that, so I constructed these notions of putting these ingredients together to give you new constructions of string theory. So that was F-theory.

Zierler:

Sure, sure.

Vafa:

Thank you. Yeah, so, where were we? I forgot. F-theory we said?

Zierler:

Yes.

Vafa:

Yeah, so F-theory, so that gave us new constructions of string theory and it is in some sense one of the most promising candidates for connecting 4D physics to particle phenomenology in the context of string theory compactifications. So many people are currently working on different aspects of it.

Zierler:

Did you have collaborators for F-theory?

Vafa:

No.

Zierler:

This is unique. You usually work with people.

Vafa:

Well, that's one example. The other example, the Swampland which I mentioned. Again, it was no collaborators.

Zierler:

Cumrun, when did you start to see that your research would be valuable for cosmology?

Vafa:

Well, I think in late eighties. I don't remember, '88 or '89, we wrote this paper with Robert Brandenberger. This was a work related to the following observations. I was always enamored with cosmology. So, I always found Big Bang mysterious. Especially the issue that there is this horizon problem that the lights that are coming to you from different directions were never in contact. In the Big Bang cosmology, well as long as you assume that Big Bag cosmology is true all the way down to zero- an assumption which did not sound very reasonable. So, the question was what happens to this assumption in the context of string theory, when you go back to the early universe? So, in mid-eighties, right, after I learned about string theory, I was asking these kinds of questions. What about string theory cosmology? And so, at that point, I already learned very early on this duality called T-duality, which is the symmetry between exchanging a big circle and small circle. It turns out string theory in a large space of radius r and a small space at radius 1/r in string units are equivalent. And to me this was really remarkable. So, I was interested in using this symmetry for cosmology. There is this beautiful symmetry that big and small are equivalent in string theory. So, if big and small are equivalent, that means big and small universes are equivalent. In other words, when the universe was getting smaller, then it's equivalently getting bigger. So, I said, okay, let's model the universe like a periodic box and see what happens if it gets smaller. So, we said if you make the universe smaller, the universe is equivalently expanding, so there is no Big Bang, period. So therefore, we wrote this paper about the idea in the context of string theory- Big Bang is totally remodeled. That you have to come up with the understanding of what happens in this small size. We were a bit more ambitious. We were trying to say, let’s also try to explain more than that. Let's try to explain why we have only three dimensions, because string theory has nine-dimensional space. Why do we only see three large dimensions? What about the other six? And the idea we had was, why don't we start with a nine-dimensional box, and for the nine-dimensional box to expand, since you have these strings which are stretched across the different sides of the box, in order for it to expand, these strings have to get annihilated because otherwise because of their stretching they become more and more massive. But they won't annihilate each other unless they find each other. So, for the strings to find each other, two strings should cross. So, a string [moving] in spacetime spans a two-dimensional sheet, and other strings spans another two-dimensional sheet and two and two meet in four dimensions, but not higher. So, a two-dimensional worldsheet and a two-dimensional worldsheet moving in a spacetime dimension more than four miss each other. So that means that if your dimensions are bigger than four spacetime dimensions, the strings won't find each other, so therefore only at most four dimensions can get big, because otherwise they won't find each other to annihilate and to relax and allow the universe to expand. So, we combined this idea with the idea of equivalence of the small and large universes, to write our string gas cosmology model. And so, I still have interest in that direction. I have, in fact, recently written some versions, extensions of that same idea in a paper with a few other colleagues last year.

Zierler:

Kind of a broad question, what have been some of the key advances in observation, in the world of observation that may be relevant and valuable for your research?

Vafa:

Well, clearly, the most important observation for string theory in recent years in the context of cosmology, is the discovery of dark energy. And the observation that the dark energy is not zero, is a big surprise for us because it's so small, but not zero, that has basically made theorists think very hard about what's the reason for it. And if it is not zero, how can we fit it in our models and what kind of models in string theory can accommodate it? And this relates to some of my more recent works in the past three, four years where I've focused exactly on the question about dark energy and present cosmology in the context of string theory. And in the context of the Swampland program.

Zierler:

What have you been doing in the recent years? As string theory has developed?

Vafa:

Well, I think, well it depends on what recent years means, but let's say after the black hole work and all that. I basically worked on two general directions in string theory. One is understanding what kind of quantum system we can get from string theory. What kind of field theories we can get, what kind of new field theories we can get in string theory without gravity? In other words, even though gravity was part of the raison d'être for string theory, but it turned out that we learned about things that have nothing to do with gravity from string theory by looking at objects and higher dimensional membranes and the properties of what lives on them, as well as studying singularities of string compactifications, what kind of new degrees of freedom emerged from that. So, it taught us about new quantum mechanical systems, or quantum field theory systems, and so I focused quite a bit of my effort on the relation between geometry and the branes and these new systems. And so, they arise in six dimensions, as the maximum dimensions, and you can have in five dimensions and so on and go down. So especially the six and the five-dimensional ones are novel. And so I spent a lot of effort trying to understand these aspects of these six and five dimensional theories, as well as in four dimensions, trying to take the garden-variety field theories that we are familiar with, gauge theories, Yang-Mills theories, coupled to matter, and realize it in terms of geometries of Calabi-Yau or some other geometrical objects. And trying to use this interplay between geometry and field theory to gain insight into strong coupling dynamics of field theories. That's one general area I have been interested in over the years, which has nothing per se to do with gravity. It's broader. It's what we learn from string theory, but it's about field theory. Then I've also been interested in trying to understand what are the defining properties of quantum gravity, and this is the work since 2005 that I initiated in the context of the Swampland program. What are the distinguishing features of field theories that are allowed to arise in gravity? Not all of them can arise. And trying to understand those better and that has become connected with the questions of dark energy, with early universe, with what happened at the beginning? Can we have an inflation, can we not have it? What about the dark energy? Is the dark energy stable? Is it decaying? What is the possible lifetime of our universe? Do we have any predictions? Those are the kinds of questions I have been more recently been working on.

Zierler:

Cumrun, have you ever embraced computers? Have computers been useful for you specifically with your research?

Vafa:

Well, I'll give you just two examples. I'm not very good at computers, but I have used them in a very amateurish way. One of them was in the context of this project about counting curves for the topological strings on Calabi-Yau. This is the work I told you, this 150-page paper with Bershadsky, Cecotti, and Ooguri. For that, we had to compute how many of these curves we get. We used Mathematica. So, Mathematica, was kind of very important for that project, involving big numbers, and it was interesting to get integer numbers that we recognized, in terms of geometry.

Zierler:

You're talking about Stephen Wolfram's program?

Vafa:

Correct. Stephen Wolfram's Mathematica program. So that we used quite effectively in that context. It was very helpful. So that was one area where I can say that computers impacted my research. Another time it impacted my research was like five, six years ago, I was working on a project, and we had come up with a calculation which gave you a power series, which again, it looked to be some part of a modular form. Like a q series expansion with some integer coefficients. And I didn't recognize what it was. So, we had computed the first four or five coefficients, and I didn't know what modular form it may be. I didn't know what to do. So, I googled it. I put the first few coefficients of this power series in Google to see what comes out, and Google connected me to a paper in physics, which didn't get exactly those coefficients that I had, but four of them were there, and the fifth one was different. And I looked at that thing and that reference. It ended up to be a modular form indeed, and moreover, it gave me a way to make them match exactly by dividing by some factor which they didn't have, or they did have, I don't remember. So that googling actually helped me tremendously with that other project! So, I think these are two examples where computers have helped me, maybe one of them inadvertently, or whatever you might want to call it, but nevertheless, it was crucial in doing theoretical physics research. But I have not done otherwise any serious theoretical computational work.

Zierler:

Cumrun, as you said earlier, that when you got involved, string theory was the domain of younger physicists. Obviously, you're a senior person in the field now. What are some of the most exciting things that your graduate students have been doing over the past decade or so?

Vafa:

Well, my graduate students, I mean, if you're asking my graduate students, they're closer to what I do. So therefore, not too different from what I have been doing because they started with me and then maybe they branch out and do other things, but at least they are not too far from the kind of things that I have been interested in. So, their areas of work would be just extensions of similar things that I have been working on myself. But if you're asking more broadly, how about younger people, whether or not they are my students, that's a different question. So, if you're asking that question, I think a lot of young people have been working on aspects about holography in the context of not just black holes, but more generally in the context of AdS/CFT, and the context of quantum information problems. So many, I would say, a large bulk of string theory research now is being done in the directions related to quantum information in some form or the other or trying to reconstruct the dictionary of holography. So that's been one of the areas. There's some area which of course I started working on it related to black hole and entropy and holography, but I have not myself worked on these areas recently. So that's one of the areas that many young string theorists have been working on, but I have not.

Zierler:

Cumrun, I'd like to ask some, sort of, sociology of string theory questions now. So, as you say, back in 1994 at Harvard, you're essentially all by yourself. In terms of the demographics of string theorists in faculties, in physics faculties, what has been the rough ebb and flow over the past twenty-five or so years in terms of when there was a real burst of new hires in string theory? When did that sort of come down a bit? And where are things now?

Vafa:

I would say that the only burst I remember was during the second revolution, which is 1995-6 area. That was the time where, for example, we hired Andy Strominger for our department, and then we have had later hires too, but I would say there has been no burst, or I would say nothing died either. So, it's kind of like steady. But the only burst I remember was that. I mean, there's always a little bit of a question mark for some colleagues about our field, because it has not connected to experiments. And so, they naturally ask, "What does it have to do with physics?" And so, we always have to justify what promise it holds for physics and what kind of theoretical ideas have come from string theory, and what kind of unifications of different branches of physics are happening within the context of string theory, even more broadly than quantum gravity. So, the broader lessons we have learned from string theory, the topological ideas, connections of holography with other areas. So, I would say that the very fact that new ideas are blossoming from string theory has been the reason it has continued, despite the fact, despite the striking fact, there has been zero experimental connection. So, I think that to me is a sign that the subject is so rich that people, colleagues who are not even working on this area, realize that something is going on in this area. It's not like people are fooling themselves. There's some spring of new ideas that connects different things in physics that is rich. We haven't been lucky to have experimental verifications because of the nature of the questions that we are interested in. Namely the fundamental questions of very small scale or very high energies, which are out of reach of today’s technology, so they realize that. So, they are tolerant towards that. And on the other hand, the mathematicians have become interested in string theory. It has clearly impacted their field. Many ideas in string theory have broad implications. One of the areas I worked on was mirror symmetry. We conjectured this based on very "flimsy" evidence from string compactification. You see by this time; I have come to the opposite side compared to my youth. I easily have physics intuition and it overrides my math intuition, that completely flipped from my graduate student days. So, I have become a very, very fierce proponent of conjecturing ideas when we have good evidence and physical intuition for it. And we conjectured that for every Calabi-Yau, there's another Calabi-Yau with cohomologies flipped, like a mirror of each other. And so when I first discussed this with mathematicians, for example with Yau, he told me that doesn't sound right, because mathematicians know more Calabi-Yau spaces with negative Euler characteristics then Calabi-Yau, with positive Euler characteristics. So, they don't seem to be equal in number. Whereas the mirror symmetry flipped all the characteristics and so had to be equal. Nevertheless, we were bold enough to make this conjecture, that there is this symmetry, the mirror symmetry. Later on, physicists, including my student Plesser and our postdoc Greene, constructed these explicitly, and non-trivial examples of it emerged, which was extensions of the small-large duality that I was working on the context of string gas cosmology that I mentioned earlier, which was my motivation for mirror symmetry. When more examples of it were emerging in mathematics, and mathematicians became more interested, I was not surprised anymore. I was kind of saying, "Yeah, of course." But rigorous proof of it still doesn't exist. So, mathematicians have not been able to prove rigorously mirror symmetry. So therefore, it is an example of my confidence and physical intuition as the spring of new ideas in math. And so, by this time, mathematicians have appreciated the use of string theory ideas. And so, a lot of them, they are open towards joint appointments in physics and math. So even though in our departments, we haven't had joint math-physics appointments, but in other universities, there are similar appointments which are in joint areas in math and physics. So that's part of the appreciation that the mathematics and physics in the context of string theory are very much intertwined, and they have this symbiotic relation, and one feeds into the other, and it's good to have them connected together. So that's I think, in answer to your question, that's another area which has grown over the years, which wasn't there. This joint area of math and physics.

Zierler:

On that basis, both that string theory has become increasingly valuable to mathematicians and as you said, in the world of experimentation, there still remains that gap in terms of what can be observationally seen. Right? So, all of that leads of course to a criticism that you know well, that after forty-plus years, what does string theory really tell us about the natural world? First, do you reject the premise of that question? And if you're bothered to answer it, what are some of the most effective responses to it?

Vafa:

Yeah so, I think that I certainly believe that that's a well-posed question and criticism for string theory. What kind of predictions are you making for the real world? Can you actually come up with something which is refutable or something that you haven't seen in the universe or something that actually is non-trivial in terms of observation? Quantitative observation. So that's a good and valid criticism. Now, some of my colleagues point to the fact that, look, if you take a pen and drop it, it drops down and there's gravity. And [the] graviton is one of the predictions of string theory! I would say, okay, fine, a graviton is a prediction of string theory, but I wouldn't say it's one of the most quantitative predictions. You want to have a little more than that. So, you want to have something more quantitative. So, in the context of this program, the Swampland program, people actually have come up with quantitative predictions of string theory which could in principle have falsified string theory, which hasn't. So, I'll give you one example. Using these ideas of Swampland program, we came up with an idea, what's called the weak gravity conjecture. Which we have evidence for, and we understand why, kind of, it has to do with black holes, that the gravity is always the weakest force. It's not just in our universe, but in any putative universe, gravity should be the weakest force. Now, using this idea, you can actually put a bound on the mass of the electron. And it turns out that the bound that you get on the mass of the electron in the fundamental view is basically in terms of fundamental units, Planck units. You find this less than ten to the minus one, but much bigger than ten to the minus thirty-one. So, you have a wide range of a prediction for the mass. It's not a sharp prediction, but still a range. Namely that you find the mass of the electron is less than ten to the minus one in Planck units. But bigger than ten to the minus thirty-one. And what is the mass of the electron? It's ten to the minus twenty-three. Okay, so it passes the check. Now, this check had to do- so you have what goes into this prediction, and you use the dark energy. So, you use the value of the measured dark energy, you use the value of the fine structure constant, and this gives you these parameters, ten to the minus one and ten to the minus thirty-one. And the ten to the minus twenty-three is the mass of the electron. It is not a sharp prediction, but it is a quantitative prediction of our universe, and it holds. Now a criticism might be, okay, this is a postdiction. You knew the mass of the electron, and therefore you could say one would not have published a paper making this prediction if it wasn't correct. So, it cannot be viewed as a prediction, but a postdiction. So one would like to have predictions, more predictions of this nature, in string theory that actually have not been tested yet, that can be tested... so some of them have to do with the nature of the dark energy, and the nature of the lifetime of the universe which are predictions now, which we can predict...which we can test in the future. Maybe it's a long time in the future before we can “experiment” these, but still the experiments that people are doing to see whether the dark energy is changing in time, which is one of the things that seems to be very natural in string theory, is one of the possible avenues to connect to string theory. Another avenue is cosmology. So, inflation seems to be not very natural in my opinion in string theory, and here is where some of my colleagues differ. And have a different view of the role of inflation. So, some of my string theory colleagues think inflation is perfectly fine in string theory, but it seems like very unnatural in my opinion for string theory. I tried to explain one of the motivations for string gas cosmology, why it's very different from inflation, and it involves something completely new coming from string theory at early times. So, we have been trying to come up with an idea similar to that, and that suggests that instead of inflation, something else takes place, and what kind of predictions this has. This would lead to a very different nature of the cosmological microwave background signature, and in particular whether we have gravitational imprints, tensor modes, or not. These kind of avenues people would be studying to see connections with string theory. So there are ideas on the fringes of what we can trust we know in string theory, which could have bearings on questions in cosmology, both early universe and inflation and its imprint on CMB, and long into the future having to do with the dark energy, and the fate of our universe and its lifetime.

Zierler:

In what ways do you see string theory as contributing to moving physics beyond the Standard Model?

Vafa:

For example, one of the things about the Standard Model is that the fields and particles naturally unify into bigger groups. Like SU(5) or SO(10) gauge groups, so the idea of Grand Unification of forces seems to naturally arise in the context of standard phenomenology, even though it hasn't been proven. In fact, surprisingly, the most obvious extension of Standard Model to Grand Unification, elegant as that idea is, does not quite work and has been already refuted. So, in order to come up with a Grand Unification of forces in four dimensions, you have to resort to some rather ugly assumptions at higher energy, which are not very well-motivated. Whereas it turns out, in the context of string theory, Grand Unification does happen. But it happens in higher dimensions. So, in other words, when you get to higher and higher energy, other dimensions open up. So, the unification is happening but not in four dimensions. So, this is telling you that some of the ideas are correct in the Standard Model, but the resolution is not in four dimensions. You need extra dimensions of string theory and so on. So, I would say these new ideas have actually pushed the Standard Model and its development in this kind of directions to take higher dimensions seriously. Even for phenomenology, because otherwise phenomenology has problems. Grand Unification is not quite working. You have to resort to ugly things otherwise. But if you allow for these extra dimensions, there are other resolutions which are more natural. So that's how it impacts. Other ideas might be in the context of the Swampland program. For example, the mass of the neutrino. The neutrino is the lightest non-vanishing mass particle we know. And its mass is related to the same scale of the dark energy. If you take the dark energy, it has units of energy to the fourth. If you take a quarter power of it, it's exactly or very much in the ballpark of the mass of the neutrino. Is this an accident? Well, it naively sounds accidental from particle physics, dark energy has nothing to do with the mass of a particle. You can choose that independently. However, in string theory, they seem to be related. And so, there are arguments, again related to Swampland, which suggests that the mass of a neutrino is pegged or related to this dark energy in some form. And so, it's not an accident that these things are related. So these ideas in Standard Model what the dark energy is and what is the origin of mass hierarchy, and what is the nature of grand unification of forces, seem to fit in these ideas of the string landscape and some ideas related to the string Swampland.

Zierler:

As you know, Cumrun, of course, one of the other key criticisms of string theory is that it's essentially not testable. To push that question to its outer limits, we can discuss the testability of the multiverse as a testable phenomenon. Where people like Andrei Linde think that is it. What are your perspectives on that?

Vafa:

Well, I think by "multiverse" if one means that there are other universes that exist, I think that whether or not it has testable consequences in our universe is unclear. It could be. For example, where did we emerge from? Where did our universe emerge from? This could be another universe with other properties most likely. So that would be perhaps imprints in our early universe. That's certainly an interesting avenue to study. So, I believe that, yes, indeed, early universe imprints. Not like Andrei would want to think in terms of inflation, but more broadly in terms of the origin of the universe, where did we come from? The analog of the dual universe. Not necessarily something as simple as an inflation, but something more sophisticated than that. I would imagine would be some hints of string theory. So, I would say yes, there could be very much imprints of it in the early universe cosmology, perhaps in CMB in more detailed experiments. I would say yes, there are chances there. Multiverse in the sense that there are a multitude of possible universes, yes, we could see some of it. Now, if by "multiverse" you mean a universe is now happening parallel to us and you can poke and go there and so on, that's theoretical to me as to what that exactly means.

Zierler:

Cumrun, for the last part of our talk, I'd like to ask some broadly-retrospective questions and then we'll look to the future. So, one aspect of your career we haven't touched upon yet is your interest in work as a science communicator. All of the interviews you've done, all of the programs that you've been a part of. What over the years have you found to be some of the most effective ways of communicating your field of expertise, which of course is not very accessible to the broad public? What are the kinds of things that you emphasize when you want to convey these ideas to larger audiences interested in science?

Vafa:

Well, I think that in trying to convey broad ideas of science to public, first of all, you have to find ideas which you think are important or interesting enough to capture the imagination of the public. That's the first thing. Once you zoom into this, then you have to describe those in a way that doesn't alienate them from making them total strangers to the statement. So, now in doing so, of course, you'll have to sacrifice, you'll not be able to do justice to the subject from the perspective of a scientist. And you realize that you're going to sacrifice. You give analogies which are not precise, which are imperfect, and all that. You show all of that, so to speak, and then you nevertheless do it, and with the mind that you're just modeling it to give a more clear picture about something they can hang onto, the public can hang onto. So, I think the two important things is analogies and big ideas which kind of attract them. Like what is the fate of our universe? Wouldn't you like to know how long we have left to live? The whole universe, I mean. Would you be surprised if I told you the upper bound is two trillion years? Don't you want to know how we got that? Or do you want to know what happens and how it decays? So, these kind of questions like, "Wow, of course, yeah tell me, where did you get that?" So that's, you first come up with things that appeals to the public and then explain how what we have learned in science has led to an insight into that question. And can you believe that you cannot distinguish a small space from a big universe? How does that work? And so on. So, things which are not that complicated to state. So, nothing fancy in formulating them, no, no, no. None of that complicated stuff. But also, I've learned another general lesson about that, which is something in the context of the course I have devised. Actually, I devised this course based on the suggestion of my wife, Afarin, who knew that I loved puzzles and their relation to physics. I love mathematical puzzles. So, I devised this course, freshman seminar, which I teach at Harvard. I have been teaching it at Harvard in the past ten years or so, where I use mathematical puzzles as a springboard to explain some of the basic principles in physics. As I explained, physics and math and their connection has always played a role in my life. And you know, as I was growing up, I was picking up puzzles that I loved to think about- not just because they are fun, but also as I later learned, because they shed light on principles of physics. It turns out many of these puzzles can actually be viewed as mini examples of physics laws or physics principles. So, I put these in the form of a course, in terms of basically motivating them to introduce some principles of physics: how symmetry works, or how breaking symmetry works, how duality works, what is the meaning of duality, what are the intuitions on physics? How do physicists come up with ideas? So, these things I put together in the context of puzzles and trying to introduce these ideas. And I recently published a book based on that course called Puzzles to Unravel the Universe. Which I hope presents to the general public some examples of how this relation between math and physics works. It's nothing scary, it's a lot of fun. As just mathematical puzzles could be fun and interesting, so could these principles be. And you can kind of get a familiarity or interest in these principles just by getting to play with these puzzles. And so that's one way of motivating the public to learn about science. This is for the high school level, or maybe early college kind of level where they can possibly hang onto these kinds of ideas and puzzles.

Zierler:

Cumrun, last question looking to the future. To return back to this idea of the issue of testability in string theory and the gap with experimentation. There are physicists, prominent physicists, who today say, "I've lost patience. It's been forty years, I'm no longer interested in hanging around and seeing where string theory goes." To the extent that you are even willing to engage with that area of criticism, what are the things and trends that you see happening in string theory that would be an effective rejoinder to that? Saying, "Actually, you should be patient. You should hang on. You should see where the field is headed, because I'll tell you exactly why it's worth the wait."

Vafa:

Okay, so two questions. First of all, there are two ways I could answer this. First of all, whether they themselves are interested, or whether they're patient enough to let others work on it. They are two different things.

Zierler:

Fair.

Vafa:

So, I would not insist anybody should work on string theory, that's number one. Indeed, it is a long-term proposal. And even though some students come to me, they ask me, "Should I work on string theory?" I say, "It depends on whether you're interested or not. And bear in mind, this is a long-term proposition. You may not see the effect in your life." People may not find it appealing, and I can perfectly sympathize with that viewpoint. You don't want to do something that by the end of your life, you don't see any impact in anything. So, why would you want to do that? I would have a lot of sympathy for people who say I don't want to work on this just because of that. I would understand that, and I would perfectly respect that. Now, if that group says nobody should work on it, then I have problems. So, that's the secondary question, or if they say, "You know what, I'm a professor in physics. I'm not going to support funding in this other field, so younger people or other people who are interested in this field would be suppressed." That I have a problem with. So, I will answer that part of your question. How would I argue against that? That they should be more sympathetic in supporting research efforts in the direction of areas of string theory. So, to explain that one has to keep in mind that string theory has a life of its own and it has spun a lot of new ideas already, that have connections with the actual world. So, in physics, one thing we love a lot is toy models. We always take [the] harmonic oscillator, we beat it to death- different versions of it in different contexts and so on. We have no problems with simplifying. The spherical cow is an example. So, this idea that we take something, and you model it and you use this to get some insight into something else is our bread and butter. Modeling is what we physicists are good at. The least you can look at string theory is a model of a would-be quantum gravity of would-be our universe. That for sure. And far more than that, it's a calculable model in many regimes of parameters. So, if you want a model, this is a model. Work on it. If you don't believe it has anything to do with actual world, view it as a "toy model." Because we have no other toy model for quantum gravity. Now-

Zierler:

But you don't believe it is a toy model?

Vafa:

No, no, I don't.

Zierler:

You think it's something more.

Vafa:

I'm just trying to motivate people who have this extreme view that string theory should not be studied. The other extreme it could be said that, no, I love toy models, but I don't like toy models on quantum gravity. Because quantum gravity has nothing to do with observations yet. So, I want to do other toy models which has to do with particle physics or something that I can measure. I would say that if you are interested in particle physics, like gauge forces, like what you see in large hadron collider, then you should still be interested in string theory, because this gauge theory gravity dualities, for example, will tell you something deep about some of these gauge theories which are not exactly the gauge theory you're seeing in an experiment, but very close to it, like a toy model, you can study it. So, it gives insight also to those. So, I'm just trying to come from a devil's advocate who doesn't like gravity or quantum gravity or doesn't believe string theory is necessarily the correct theory of quantum gravity of our universe, and just focus on actual experiments, why those physicists should be more tolerant. So, I'm giving the answer to that group. Of course, I believe string theory is the correct theory of quantum gravity of our universe, but I don't have a proof for that, so I cannot say, "Believe me, trust me." Because they say, "I don't trust you, I don't believe you." Okay. So, giving example after example will not necessarily convince them. But if you say, "Look, a toy model for it, you believe SU(3) is QCD?" "Yeah, I do." "Okay. Do you believe Fermions [are] there?" "Yeah." "Okay, you think that there could be matter in different representation of SU(3)?” "Well, they could be, but not in our universe." "Well, let's say it's a toy model, we take this and that, and make it a supersymmetric theory. And suddenly we can say so much about it that we didn't know, and this comes from string theory. Okay." Now, this is the kind of thing I think that they certainly cannot have an objection to. So, development and understanding, the deeper understanding of these ideas, are crucial.

Zierler:

Cumrun, it has been great fun talking with you today. I'm so glad we were able to do this. Thank you so much.

Vafa:

Thank you so much, David, for these fantastic questions. it brought back so many good memories from older days. Maybe too much emotion, but at any rate.

Zierler:

Ahh, that's great, wonderful.