John Schwarz
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ORAL HISTORIES
Credit: Brigitte Lacombe
Interviewed by
David Zierler
Interview date
Location
Remote Interview
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Interview of John Schwarz by David Zierler on July 7, 2020,Niels Bohr Library & Archives, American Institute of Physics,College Park, MD USA,www.aip.org/history-programs/niels-bohr-library/oral-histories/45439
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Abstract
In this interview, David Zierler, Oral Historian for AIP, interviews John Schwarz, Harold Brown Professor of Theoretical Physics, Emeritus, at Caltech. He describes his family background as a childhood of European emigres, both of whom were scientists, and who escaped Nazi persecution at the beginning of World War II. Schwarz recounts his childhood in Rochester and then on Long Island, and he describes his undergraduate experience at Harvard, where he studied mathematics. Schwarz explains how his interests in the “real world” drew him to physics, which he pursued in graduate school at Berkeley and where he worked with Geoffrey Chew on pursuing a theory of the strong nuclear force. He explains Chew’s conclusion that quantum field theory was not relevant toward developing a theory on the strong nuclear force, and he proposed, alternatively, the S-matrix, which in turn was overtaken by the Yang-Mills gauge theory known as quantum chromodynamics. Schwarz explains how Veneziano’s Eular beta function grew out of the S-matrix program, which extended into a new theory called the dual resonance model, which came to be known as string theory because the model was understood as a kind of quantum theory of one-dimensional objects called strings. Schwarz recounts his contributions to these developments during his time at Princeton, where he collaborated with David Gross, André Neveu, and Joël Scherk. He discusses the significance of Claud Lovelace’s work at CERN, where he found that singularities could be made into poles, and he explains how the second string theory came about in 1971 which required ten spacetime dimensions. Schwarz explains why string theory was not part of the work Glashow and Georgi were doing to unify the three forces of electromagnetism, weak interactions, and strong interactions within a larger gauge symmetry. He describes Feynman’s reluctance in accepting QCD but why, in the end, it proved to be the superior way to explain the strong nuclear force. Schwarz describes his decision to join the faculty of Caltech with the encouragement of Gell-Mann, and he explains the ongoing value of string theory even with QCD firmly established, because it gives gauge theory interactions. He recounts the “second revolution” of string theory in 1984 and his work with Michael Green, and he describes the initial optimism that supersymmetry would be discovered with the advent of the LHC. Schwartz describes Ed Witten’s rising stature in the field, and he shares his views on why thousands of people remain captivated by string theory today. He provides a response to the common criticism that string theory is untestable, and he explains the significance of Juan Maldacena’s discovery of the connection between string theory and conformally invariant field theories. At the end of the interview, Schwarz reviews what among the original questions in string theory he feels have been answered, and which remain subjects of inquiry, including his interest in new approaches to quantum gravity.
Transcript
Zierler:
Okay. This is David Zierler, oral historian for the American Institute of Physics. It is July 7, 2020. I am so happy to be here with Professor John Schwarz. John, thank you so much for joining me today.
Schwarz:
My pleasure.
Zierler:
All right. So to start, would you please tell me your title and institutional affiliation?
Schwarz:
Yes. My current title—it’s kind of a long one—is Harold Brown Professor of Theoretical Physics, Emeritus.
Zierler:
[Laughs] Now do you have any special connection to Harold Brown?
Schwarz:
Well, he was the president of Caltech when I arrived here in 1972. I had met him briefly at that point. In the last couple of years, I went to a couple of events at the Rand Corporation where he was very much involved. In fact, I just was there about a half year ago for a memorial service following his passing. But I didn't have much interaction with him in the intervening years.
Zierler:
Is the chair endowed by his family, or it’s a Caltech endowment?
Schwarz:
I don't know the details, but I believe that IBM was a primary contributor.
Zierler:
Oh, wow.
Schwarz:
But I don't know the details.
Zierler:
Okay. Good. Well, let’s take it right back to the beginning, John. Tell me first a little bit about your family background, starting with your parents. Where are your parents from?
Schwarz:
Very good. So my mother was born in Budapest, Hungary. My father was born in a region in Transylvania which belonged to Hungary when he was born, but after the First World War went over to Romania. My mother went through high school in Budapest, but that was a pretty anti-Semitic place and university there was not an option, so she went to the University of Vienna. My father also went to the University of Vienna, which is where they met.
Zierler:
Do you know what year they met, or roughly?
Schwarz:
Well, it would have been early ’30s.
Zierler:
Before things got scary.
Schwarz:
They were married, I believe, in ’34. My father was studying chemistry, and he was a specialist in photographic chemistry. My mother was interested in physics and philosophy. I think she was undecided between those two, but my father pushed her towards physics, which is what she did. I think she did some experiments on neutron diffraction or something like that. I don't know the details. In 1933 they each got PhDs there in Vienna.
My mother was offered a post-doc in Paris by Marie Curie, but before she could take up that position, Marie Curie died and her lab in Paris was taken over by her daughter, Joliot-Curie. My mother, for whatever reason, didn't care for Joliot-Curie and didn't want to work for her. [Laughing] So she got married instead to my father. So in this peculiar way, Marie Curie’s passing worked out to my benefit. [Laughter] I wouldn't exist otherwise.
After they were married, they moved to Antwerp, Belgium where my father was immediately appointed as director of research at the Gevaert Corporation, which manufactured photographic film and supplies. It was a big corporation. My sister was born there in 1935 in Antwerp, and the three of them were living in Antwerp when the bombs started falling in May of 1940.
Zierler:
Was your father Jewish also, John?
Schwarz:
Yes. His parents died when he was very young, and it was certainly a Jewish family, but he was adopted at that point by a Unitarian minister. Unitarianism is a religion that actually started out in Transylvania.
Zierler:
I did not know that!
Schwarz:
So he was raised by this Unitarian minister in Transylvania, but he was certainly Jewish. My recent DNA analysis shows that I’m 98% or so Ashkenazi Jewish. [Laughs] So I can confirm it that way.
Zierler:
I was asking more… I was curious if he was in danger as a matter of being a Jew, even if he was pretty separated from his heritage.
Schwarz:
Well, I don't know if that’s why he chose to go to Vienna. I do know that’s why my mother did, but it’s possible that it was the same reason for him. Some of the famous Hungarian physicists that we know about did go to the university in Budapest, but my parents didn't. My mother knew several of these well-known people including Szilard and Teller.
Zierler:
Amazing.
Schwarz:
She was a high school classmate of Teller’s wife.
Zierler:
John, was your mother a trailblazer? I mean, was she breaking glass ceilings all the time in her capacity as a woman in that day and age, or did she have peers who were also doing these kinds of things?
Schwarz:
She wasn’t the first, but there were certainly very, very few.
Zierler:
Right, right.
Schwarz:
After she got married, she did not do research anymore. My sister was born in ’35, as I may have mentioned already, and I think she had her hands full with that in Antwerp. So in 1940 when the Nazis took over Belgium, as soon as the bombs started dropping, my father and mother grabbed my sister. They had a car. They left all their worldly possessions. They said, “We don't have time to worry about such stuff.” They got in their car and drove to Paris, where my father thought he could help the free French. That didn't last very long, but they were in Paris for a month or two. Then they, with considerable difficulty, worked their way through from southern France to Spain and Portugal and got on a ship to Rio de Janeiro.
Zierler:
Was your sense that they were specifically fleeing the Nazis as Jews—they would have been deported otherwise—or were they more broadly just trying to get away from the war?
Schwarz:
I think it’s mostly the former, but both. Both. My parents did not talk much about this.
Zierler:
Yeah.
Schwarz:
I knew that we must have had many relatives that died in the Holocaust, but if you had asked me a couple years ago to name them, I wouldn't have been able to. I know more now because my sister has been doing ancestry research on the Internet.
Zierler:
Oh, wow. Okay. So it was Rio. That was their first stop in the New World.
Schwarz:
Right, and the reason they went there was that the Gevaert Corporation had a branch there.
Zierler:
Oh!
Schwarz:
So my father was immediately employed. In fact, I think he was made director or something similar there.
Zierler:
Amazing.
Schwarz:
But they only stayed in Rio for a few months, and then they went to Massachusetts. They lived in Williamstown, Massachusetts, where Williams College is located.
Zierler:
Was your sense that Brazil was always a layover on the way to the United States?
Schwarz:
I don't know whether they knew they would be going to the US when they left Europe, but after a few months in Brazil, they made this move. Gevaert had another office in North Adams, Massachusetts and Williamstown is just a couple miles from North Adams, and so they went there. My father was made director again, so he was well employed.
Zierler:
Did the company sponsor his exit visa?
Schwarz:
I doubt it, but I don't know.
Zierler:
So they really -- As far as you can tell, they might have just gotten on a boat and hoped for the best without any guarantee that they would be even accepted in Rio.
Schwarz:
Well, they had the employment. He knew he had employment.
Zierler:
Okay, okay. That was waiting for him.
Schwarz:
Then when they went to the US, he knew he had employment in North Adams, Massachusetts, so that’s why they went to these specific destinations.
Zierler:
When did they gain citizenship?
Schwarz:
I think it was five years after they arrived in the US. His affiliation with Gevaert didn't last very long, because he quit when it became clear to him that they were collaborating with the Nazis, which they had to do. They were occupied, after all.
Zierler:
Right.
Schwarz:
It doesn't prove they were evil; they had no choice in the matter.
Zierler:
My father still doesn't buy Ford automobiles, so you know, these things run deep. [Laughter]
Schwarz:
Right. So anyway, he continued doing photographic chemistry research for a variety of other companies after that.
Zierler:
And then when do you arrive on the scene?
Schwarz:
Okay. So I was born in November 1941, which is about a year after they arrived in the US. So I guess I could say I was conceived in the US as well! [Laughing] I was the first US citizen in our family.
Zierler:
Did your family stay in western Massachusetts?
Schwarz:
So they moved around ’45 to Rochester, New York, where he worked for a couple of different companies. One was Bell and Howell, and then he was also involved with a small startup that failed. In ’50 or ’51 he got employment at a company in Glen Cove, New York, which is in Nassau County, Long Island. He was made Director of Research again. They did photographic chemistry, as well, and he made the owners of that company very wealthy.
Zierler:
What was his contribution?
Schwarz:
Well, he made all the inventions. Of course, all this stuff is obsolete now. Chemistry is irrelevant for photography in the modern world.
Zierler:
Right.
Schwarz:
[Laughs] But he was a leader in it nonetheless. Everything is digital today.
Zierler:
Did your father consider himself a scientist? Would he have used that word to identify himself?
Schwarz:
Oh, sure. Sure.
Zierler:
Yeah. I mean as opposed to an inventor or a businessperson. He was primarily a scientist.
Schwarz:
Yes, absolutely.
Zierler:
So was it in Long Island that you spent your formative years growing up?
Schwarz:
Yes, when we moved to Long Island, I was in fifth grade, I believe, and I stayed there through high school, all public schools on Long Island. I had had a couple of years of private school in Rochester, but otherwise it was all public schools. The public schools I attended on Long Island were good but not fantastic. It was adequate. In those days they didn't teach calculus in high school yet.
Zierler:
Right.
Schwarz:
So that kind of dates me because nowadays everybody learns calculus in high school. I learned some on my own, but not a lot.
Zierler:
Sure. John, did your parents involve you in their scholarly interests? In other words, was science sort of in the air in the household?
Schwarz:
Well, they were extremely supportive and it was clear they were scientists. My father would judge science fairs at the high school and do things like that, except when I was a contestant and didn't want to have a conflict of interest. My mother would always tell the guidance counselor how to do his work because he didn't really know. [Chuckles]
Zierler:
Did they encourage you to--
Schwarz:
They didn't try to push me ahead. In Rochester I skipped third grade. I think what happened there was that when I was in second grade they gave us an IQ test and I got every question wrong. So my mother asked me why this happened and I explained to her it was a stupid test. [Laughs] I did it on purpose, and then they put me in fourth grade.
Zierler:
Were you a stand out in math and science in high school?
Schwarz:
Yeah. I mean, it wasn’t an exceptional high school and standing out there didn't prove I was going to be successful. [Laughs]
Zierler:
But it was enough to get you to Harvard.
Schwarz:
That’s right.
Zierler:
When you went to Harvard… First of all, what other schools did you apply to?
Schwarz:
For undergraduate.
Zierler:
Right.
Schwarz:
Yes. The place I most hesitated about vis-à-vis Harvard was Caltech. I was accepted to both and to a few other places that I won't bore you with, but my choice boiled down to those two and it was a difficult choice.
Zierler:
And the plan was mathematics. You wanted to study mathematics as an undergraduate.
Schwarz:
Yes. That was my undergraduate major. At every stage in my career I sort of knew what the next step would be, but I didn't know what would happen two steps ahead. I was pretty sure I wanted to do math. Going to the West Coast was a bigger deal in 1958 than it would be in the modern world. [Chuckles]
Zierler:
Right.
Schwarz:
So Harvard was closer to home. Also, even though I knew I wanted to do math and science, I thought…and my parents pushed me this way too, I think. I thought it would be good to be exposed to a broader group of fellow students with other diverse interests. So I’m glad I made the choice I did, and on occasion I have advised others this way against Caltech’s interest. [Laughing] It’s kind of ironic, because I’ve done a lot of work for Caltech undergraduate admissions. [Laughs]
Zierler:
John, I’m curious. I mean, to just fast forward into your later work in string theory, in superstring theory, many physicists who start out in math come to the conclusion that it’s sort of just too abstract and they need something a little more hands-on. But I wonder for you if you were comfortable in the more abstract realms of math and that going to physics was not necessarily about getting more into the real world, so to speak.
Schwarz:
Well, dealing with abstractions is hard.
Zierler:
Right. For sure!
Schwarz:
I know when I learned things that seem very simple to me today that I struggled with them. So I don't think I could have been a leading mathematician. I think I could have been an average mathematician [chuckles], but I don't think I could have been a leading mathematician. But that wasn’t really what forced my decision. It was more the other thing you said, which is relating to the real world.
When I was at the point of deciding what to do in graduate school, my thinking was that math is fun, but I don't really understand how mathematicians choose their problems and what it is they want to achieve, whereas in physics it’s clear that you're trying to describe the real world. So that was my thinking at the time. I think today I do understand what mathematicians are up to better than I did then, so I wouldn't phrase it that way today, but that was my thinking back then.
Zierler:
How much physics did you take at Harvard?
Schwarz:
Yeah. Just as they didn't teach calculus in high school back then, they didn't teach quantum mechanics to undergraduates back then.
Zierler:
Oh, wow! Math for physicists.
Schwarz:
Yeah. So it was really a different world.
Zierler:
Yeah.
Schwarz:
But I was fairly advanced and I took quantum mechanics my senior year, but it was a graduate-level course. Today it would be an undergraduate-level course.
Zierler:
Do you remember who taught it?
Schwarz:
Yes. It was Kurt Gottfried. He was an assistant professor who didn't get tenure; he went on to Cornell…
Zierler:
[Laughs] Their loss.
Schwarz:
Yes, he did very well.
Zierler:
Right. Right. At what point, John, did you know that you wanted to switch over to physics for graduate work?
Schwarz:
Well, I can't pinpoint it, but it was probably in my junior year.
Zierler:
And on that basis that you wanted to work with things that were more part of the real world.
Schwarz:
Yes.
Zierler:
Did you go to Berkeley specifically to work with Chew?
Schwarz:
No, I hadn’t even heard of him. So all this is very weird, but I applied to three places for graduate school. They were Berkeley, Caltech, and Princeton, and Caltech and Princeton rejected me, so that made it very simple. That’s why I went to Berkeley! [Laughs] Had all three accepted me, I’m not sure what I would have done.
Zierler:
Right.
Schwarz:
But I didn't have to make that decision.
Zierler:
Do you think with Caltech and Princeton not having a physics undergraduate was part of the decision? Would there have been a bias against non-physics majors?
Schwarz:
Maybe. I served on the graduate admissions committees both at Princeton and Caltech subsequently. [Laughs] So I have unusual insight into these issues. In fact, in Caltech’s case, I even chaired graduate admissions in physics for about six years. So there are all sorts of weird stories here, which are not terribly important, but are funny.
Zierler:
That’s half of what I’m in this for. I love it. Please!
Schwarz:
[Laughs] The fact that I didn't specialize in physics may account for why I got a relatively mediocre score on the physics GRE, a score which, based on my later experience, I would say was borderline. So that would be, I think, the main reason that it went that way.
Zierler:
Well, it worked out pretty well.
Schwarz:
Yeah. Now… I have always felt, when I was doing admissions work too, that these GRE tests are next to useless and deeply flawed. By the way, my sister worked for ETS, the outfit that makes these tests, in Princeton. [Laughs] But her specialty was foreign languages, so I can't blame her for anything in the sciences. The problem is that the physics GRE really focuses on things that you learn in freshman and sophomore physics, and they give you lots of short questions which you have to answer very quickly. So if you have to think it through—say you're capable of figuring it out, but you don't have it on the tip of your tongue—you're not going to finish the exam in time.
Zierler:
Right, right.
Schwarz:
And if you're someone who is advanced and has been taking advanced stuff for most of your undergraduate career, you won't do well on that unless you really prepare for it and get all that stuff so it’s on fast recall. So a lot of very good students don't do particularly well on the physics GRE. That said, I think if that happens to people, it’s not the end of the world. As in my case, I believe for other people, as well, they’ll end up at some good place, and if they’ve got what it takes, they’ll emerge with no harm done. You don't need to go to Caltech or Princeton to be successful.
Zierler:
John, what were your impressions of Berkeley when you got there?
Schwarz:
Well, it’s a great place and I really loved it. My first year I lived in the International House, so I was exposed to a very interesting group of people. The International House in Berkeley has about 500 residents and they’re half US citizens and half from all over the world. So that was a great thing. At that time, Berkeley had about 400 graduate students in physics.
Zierler:
Wow! Probably the biggest department in the country.
Schwarz:
Probably, yes, which is more than they have today. I don't know what the number is today, but certainly less than that. Perhaps half.
Zierler:
Well, this is definitely the post-Sputnik generation. I’m sure that has something to do with it.
Schwarz:
Yes, yes. In the mid-’60s, the field was undergoing exponential growth, and like all exponentials, it ended at some point [chuckles] rather dramatically. So I didn't know even knew who Geoff Chew was when I arrived at Berkeley, but after I was there, I learned that he had these exciting ideas and was a great student advisor. He had about ten graduate students working with him, and so I worked with him, too. I started in my second year doing research with Chew. Berkeley had some good assistant professors, too. Sheldon Glashow and Steven Weinberg were both assistant professors. I took electromagnetism from Glashow and I learned a little bit of field theory from Weinberg. I also took courses from Mandelstam and Chew and more phenomenology-type things from other people.
That was an exciting place to be. Berkeley was very highly regarded in that era and it still is, but even more so, perhaps, back then. Chew was really quite inspirational. He had this vision. He was sort of a prophet. I was very strongly influenced by him in my thinking, which had good aspects and less good aspects. Another Chew student who entered and graduated in the same years as I did was David Gross. We were both there for four years, and the last three years we shared an office, so I got to know David pretty well. We had one coauthored paper as graduate students.
Zierler:
Do you remember what you worked on with him?
Schwarz:
Yes, I do. It’s not a famous work, but I thought it was pretty clever at the time. [Laughing] It was very esoteric. But you can find it. [Laughing] It’s published in Physical Review, I believe. We had this wonderful office. I didn't know it at the time, but what happened was Berkeley was trying to hire Murray Gell-Mann.
Zierler:
Right.
Schwarz:
That was top secret, so I didn't know it. They had just built--
Zierler:
Any idea who the driving force was behind that?
Schwarz:
I don't. Chew would have certainly had a say in the matter, but I don't know whether or not he was the driving force because, as I say, I didn't know about it at the time. I only learned about it much later.
They had just built a new physics building, called Birge Hall, which later became old and decrepit and had to be renovated, but it was brand new and sparkling back then. It had this wonderful corner office overlooking the bay on the top or second-to-top floor, which they were saving for Murray. But they had a problem, because Murray never said yes; and he didn't say no. If they put another professor in there, they couldn't get him out, but if they put in graduate students, they would be easily removable if Murray were to come. So that’s how David and I ended up in that wonderful office. [Laughing]
Zierler:
So how did you formally get to be Chew’s student?
Schwarz:
I suppose at one point I asked him and he said yes, but I don't have a clear memory of that. My memory is not fantastic.
Zierler:
What was he working on at that point (Chew)?
Schwarz:
Okay. So his program went under the general name of S-matrix theory, and the basic idea was that one needed to find a theory of the strong nuclear force, the force that’s responsible for the properties of hadrons, which are a class of particles such as protons and neutrons that undergo strong nuclear forces. At that time, such a theory was not known, and lots of new hadrons were being discovered.
Zierler:
All right. I was asking you what Chew’s research was right around the time when you connected with him.
Schwarz:
Yes. So he wanted and everybody wanted a theory of the strong nuclear force. The only fully successful relativistic quantum theory that existed at that time was quantum electrodynamics, a theory of photons and electrons developed by Feynman, Schwinger, etc. That theory depends very strongly on the idea of doing expansions based on perturbation theory where you have a small parameter, the fine structure constant. You can calculate various things as a power series in the fine structure constant, and the first couple of terms gives you very good answers. But it was known that in the case of the strong nuclear force the coupling constants are of the order of unity, in other words they are not small, and a perturbation expansion would not be helpful.
The formalism that underlies perturbation theory is quantum field theory in this context, so Chew concluded that quantum field theory was not a promising approach to developing a theory of the strong nuclear force. His alternative idea was to focus on the S-matrix, which is the matrix of amplitudes that describes all possible scattering processes, physical scattering processes. This matrix satisfies all sorts of properties—unitarity, analyticity properties of various sorts, and so on and so forth—and by exploiting these properties, together with some additional inputs which were developed in that era, which went by the names of Regge pole theory and the bootstrap hypothesis, which Chew had developed, these could take you a long way towards finding formulas for all of the scattering amplitudes.
So that was his program, and the history of what happened after that is really bizarre. Taken at face value, you could say that it was a failure, because in the early ’70s, a quantum field theory was discovered for the strong nuclear force, a theory named QCD (quantum chromodynamics), which is a Yang-Mills gauge theory based on the group SU(3), where the fundamental particles are quarks and gluons. Most of the ingredients of this theory were developed by Gell-Mann at Caltech. Certainly the quarks were his idea. [Laughs] He also named the gluons and almost everything else in the business. So in that sense, Chew’s program failed, because here was a beautiful quantum field theory that worked.
Zierler:
Right.
Schwarz:
By the way, my friend David Gross contributed to one of the important developments in QCD, which resulted in his sharing a Nobel Prize.
In the attempt to implement the Chew’s S-matrix theory program, there was a formula discovered by a young Italian physicist, Gabriele Veneziano, in 1968, where he just wrote down an explicit mathematical function, the Euler beta function, which had many of the mathematical features that the S-matrix theory program demanded: the bootstrap idea and Regge poles and analyticity and so forth. 1968 was still before QCD. I was already in Princeton then, since I graduated from Berkeley in 1966.
So this Veneziano formula led to an explosion of interest, and several hundred people extended it to a new kind of theory, which initially was called a dual resonance model. In the early ’70s it was realized that dual resonance models could actually be understood as a kind of quantum theory of one-dimensional objects, called strings, so later the subject got renamed string theory, but it started out as dual resonance models.
Zierler:
Do you know who saw this metaphor of strings and named it so?
Schwarz:
Well, there are three people who are credited as independently recognizing that there are one-dimensional objects. Which of them used the word string I couldn't say, and I don't feel that that’s an important question. Those three people are Yoichiro Nambu, Holger Nielsen, and Lenny Susskind. They recognized that the formulas could be interpreted that way.
Zierler:
How closely were you following these developments in 1970?
Schwarz:
So the Veneziano formula came about in ’68, and in the academic year ’70-’71, Chew had a sabbatical in Princeton. [Laughing] So I saw him again there. He was quite excited about Veneziano’s paper, and there wasn’t much interest at Princeton in it. But he got me interested because he realized that it was doing what his program wanted. [Chuckles] So I began to pursue that. I didn't start working on it immediately following Veneziano’s paper, but maybe 6 or 12 months later, especially after being prodded by Geoff.
I had three primary collaborators in Princeton one of which was David Gross. David wasn’t there at the beginning, because when we left Berkeley, I went straight to Princeton. He went to Harvard as a junior fellow, and then came to Princeton as an assistant professor after he finished at Harvard. I was made an assistant professor at the same time at Princeton. So he was one of my collaborators on this stuff at the time. The other two were two French guys, André Neveu and Joël Scherk. There’s an interesting story there, too.
André and Joël were the two young superstars from France, and they showed up in the fall of ’69 at Princeton. They had received training that was equivalent to a PhD, but the French system was different. Princeton didn't recognize the name of whatever it is they had. They were there on some special fellowship. So they were classified as graduate students, and as such, they were assigned faculty advisors, and they were both assigned to me.
So these two guys walk into my office one day and I hadn't met them. I didn't know anything about them. They were just complete strangers, and they said, “We’re your advisees. Can you sign our cards?” So I said, “Sure. Do you need a course in electromagnetism?” They said, “No, we’ve already had it.” “Do you need a course in quantum mechanics?” [Laughing] “No, we’ve already had that.” So I said, “Okay, I’ll sign your card,” and then they went away.
Then a few months later they show up again in my office and they say, “We have some results we would like to show you.” What they had done was the first calculation of one-loop amplitudes in string theory. There were some divergences for which they did a brilliant mathematical work that involved using Jacobi transformations to isolate the leading singular behavior, and it was beautiful work. So at that point I was quite convinced they didn't need quantum mechanics or electrodynamics. [Laughs] They were indeed superstars, and I had many very fruitful interactions with them in subsequent years.
Zierler:
In what ways had the dual model differed from the original model from Veneziano and his colleagues?
Schwarz:
The first formula Veneziano wrote down described a process in which there are two particles scattered and two come out, so it’s what we would call a four-point amplitude. There were many subsequent steps. The first step was to find an n-particle generalization, and that was done by several independent groups, and then to demonstrate that these n-particle generalizations had an internal consistency so that when you factorize them, at poles, you get other n-point amplitudes in a very consistent way as required by unitarity. Veneziano and Fubini were among the important people doing that. So that was perhaps in 1970.
Then Gross, Neveu, Scherk, and I did a more detailed study of the one-loop amplitudes following the original work of Neveu and Scherk that I discussed, and there are several different kinds of amplitudes. Once one has the string interpretation, one can think of an open string that forms a loop. This gives a cylinder. That’s a loop of open string. Or it can form a Möbius strip, which is another kind of loop of open string. In any case, in the cylinder case, if you consider a four-point amplitude with two particles attached to each of the two boundaries, we did the calculation of the amplitude for that, the four of us, and we discovered that this amplitude has singularities that imply that the theory is inconsistent. That was a 1970 paper.
This prompted Claud Lovelace, who was working at CERN, to explore what to do about these singularities, and he… I’m told that he was prompted to do this work by David Olive, so I should give David credit, too. Lovelace realized that the singularities could be made into poles, which would have a consistent interpretation, if one took the spacetime dimension to be 26 rather than 4. Up to that point, everybody knew that there are four dimensions, three of space and one of time, and the idea that we’d consider any other number was absurd.
Zierler:
And when you say everybody knew, based on what? What are the bedrock principles?
Schwarz:
[Laughing] Because we know. We live it! We experience it. [Laughter]
Zierler:
You mean you don't even need to be a physicist to know we live in four.
Schwarz:
That’s right.
Zierler:
Right.
Schwarz:
So I mean, it was viewed as crazy to consider anything else. So here Lovelace comes and says, “Your formula is fine if you take it to be 26 dimensions rather than 4.” So that kind of shook us up a bit. And indeed, this original Veneziano model does require 26 dimensions to be consistent, but even then it has a problem because it’s… Well, it has lots of problems. One problem is it doesn't have any fermions, so that makes it unrealistic, and another problem is that the spectrum has a tachyon, which means that the vacuum is unstable, which is also a serious problem. So it wasn’t a consistent or realistic theory, but it was much more consistent in 26 dimensions than it was in 4.
So what we needed was another theory, and this came along in 1971. It started with a discovery by Pierre Ramond, who was at Yale at the time. What Pierre did was to write down a string analog of the Dirac equation. It was quite inspired, really. So the formula he wrote down just described free particles; it didn't say anything about interactions. But it showed that there was a beautiful mathematical structure just for the free spectrum of fermionic strings.
At the same time, I was working with Neveu. Scherk by then had returned to France, so only Neveu remained in Princeton. I was working with Neveu on another bosonic string theory, which had much of the same mathematical structure as Pierre’s fermionic theory, so our string theory is now called the Neveu-Schwarz model and Pierre’s is the Ramond model, but they’re really parts of the same theory. Ramond’s fermions and our bosons all fit nicely into a single theory, which in those days we gave some silly name that was based on our preconception that we were looking for a theory of the strong nuclear force, and that the particles we were describing are pi-mesons. So we called the theory the dual pion model. But anyway, that’s just a historical thing which is very forgettable, because the modern interpretation is entirely different.
So anyway, in 1971 the second string theory was developed for which consistency requires 10 spacetime dimensions rather than 26. My attitude at the time was that this was a step in the right direction, and our next theory would have four dimensions, but that’s not the way the history worked out.
Zierler:
John, is your sense that string theory was a perfectly logical next step from Regge poles?
Schwarz:
Well, it has a Regge pole structure built into it, so these Regge ideas are implemented in string theory.
Zierler:
I guess my question is, are there other intellectual heritages from Regge pole that are not sort of part of the string theory family, or is your sense that this is where Regge pole is headed?
Schwarz:
In the last couple of years, people who work on what is called the conformal bootstrap, which is an approach to studying conformal field theories, have found it useful to organize their calculations in ways that are reminiscent of Regge pole theory. So it has resonances there, and that’s very recent work. Actually, that whole conformal field theory story is connected to string theory, so how different it really is is another question. [Laughs]
Zierler:
Right, right. John, if I could try to isolate your memory of these heady years between 1968 and 1972, really before QCD ends the party, right, what was so exciting about string theory before QCD? What was the big promise of string theory?
Schwarz:
Well, we were trying to describe the strong nuclear force, and there were several hundred people—more in Europe than in the US, but also in the US—who were working really hard on this stuff. They were making interesting discoveries, so it was very active. There were international meetings and so on and so forth. The last big gathering of the early string theory community was a workshop I organized at the Aspen Center for Physics, which was in 1974. The community had already started shrinking at that point, but it still existed. So that was, in a way, just the tail end of it, but it was a good group of people.
Zierler:
Were you or your colleagues using terms like grand unified theory at that time?
Schwarz:
This term, grand unified theory, started with work of Howard Georgi and Glashow in 1974. Their idea was to combine the SU(3) symmetry of QCD with the electroweak theory’s SU(2)×U(1) symmetry inside of a larger symmetry group, so that there is a unification of those three forces (electromagnetism, weak interactions, and strong interactions) in terms of a larger gauge symmetry. That was interesting work, but it was based on quantum field theory and it’s not string theory. Some of the ideas of grand unification can be realized in modern string theory, but that isn't what string theorists were thinking about back then.
Zierler:
Right. So there wasn’t a motivating factor within the string theory world that this was going to get us closer to a grand unified theory, if not that exact term, but that concept.
Schwarz:
We weren't trying to unify interactions yet. We were just trying to understand the strong interactions.
Zierler:
Right.
Schwarz:
So in that sense, they were ahead of us. Or, as I will explain, simultaneous.
Zierler:
In what ways did QCD do better as an explanation of the strong nuclear force?
Schwarz:
Well, one of the arguments that Chew made for why you shouldn't do quantum field theory is that there is an enormously rich spectrum of hadrons that was being discovered, and if you introduce an elementary quantum field for every one of them, that would just give a god-awful mess that would be intractable. But that’s not what QCD does. QCD is based on the constituents of hadrons, which are the quarks and gluons, and they’re the ones that correspond to the fundamental fields, and then you have a beautiful theory, which is a Yang-Mills gauge theory based on the group SU(3). So once that became understood, people using asymptotic freedom and so on could do useful calculations, and also incorporate the ideas of the quark model and so forth. Everybody was immediately convinced that this was right. I never questioned it, either. Actually, the person who was most reluctant to accept QCD, ironically, was Richard Feynman, and that’s a whole other story which I’d be happy to tell you, but I think it would be out of sequence here. [Laughter]
Zierler:
Who cares about sequence? Let’s hear Feynman.
Schwarz:
[Chuckles] Okay! So I should say first that I left Princeton and came to Caltech in 1972.
Zierler:
Right, before QCD. This is still at the height of string theory’s promise. Right.
Schwarz:
Right, and Caltech was an exciting place to come in that era because Gell-Mann and Feynman were there.
Zierler:
Right.
Schwarz:
It was Gell-Mann who was responsible for bringing me there, and I can talk about that later if you want. But anyway, when QCD came along, it incorporated some of the ideas that Feynman had developed. He had developed what he called the parton model, which was the idea that hadrons have point-like constituents which he chose to call partons, and he developed a whole formalism for understanding electron scattering experiments that were being carried out at SLAC and other places in terms of this parton model of his.
Dick had this strange idea that physicists can get seduced by beautiful mathematics and lose track of the nitty gritty in the process. So he wasn’t going to accept QCD just because it was a beautiful theory. He had to understand it in terms of nitty gritty. [Laughs]
He had a collaboration with Rick Field, who was a post-doc at Caltech back then. Rick was great with computers and Dick had lots of great ideas, and between the two of them, they did all sorts of detailed studies of the strong interactions. I didn't follow this work very closely, but anyway, they eventually convinced themselves that QCD was indeed correct. But they had to convince themselves from first principles. They wouldn't just accept it because it was a beautiful theory.
Zierler:
How long did it take? A few years?
Schwarz:
Yeah, a couple of years, mm-hmm [yes].
Zierler:
So you arrive in Caltech in 1972.
Schwarz:
1972. So let me say a little about that.
Zierler:
Right.
Schwarz:
I mentioned exponential growth in the late ’60s and I mentioned that exponentials don't last forever, and this one came to a crashing end around ’71, ’72. People who were not that great were being hired without much difficulty in the late ’60s, but by the early ’70s there were basically no jobs available. However, Princeton had a couple of tenured positions to fill. I never thought about staying at Princeton; I was intending to leave, but in any case, they decided in ’72 that they would give tenure to Curtis Callan and David Gross. Both have had fantastically successful careers. No one would question that this was a great decision. In any case, this meant I had to leave. If it weren't for a lucky sequence of accidents, I could well have ended up without a job, at least in a good place. Actually, getting jobs in less good places was also impossible. [Laughs] It wasn’t only the top places.
Zierler:
Right, right.
Schwarz:
And then there was also the Vietnam War. That’s a whole other thing. Suffice it to say, I narrowly escaped being drafted. So what happened was that my work with Neveu caused a big stir in the theory group at CERN where they had a lot of people working on string theory (or dual resonance models). Murray Gell-Mann happened to have a sabbatical at CERN in ’71- ’72. So he got wind of this, and this led him to offer me a job at Caltech. Had he stayed at Caltech it is doubtful that he would have been aware of our work. So I was very lucky that I got plucked out in that manner at that time, because I don't know if I would have survived in the profession otherwise
Zierler:
[Chuckles] John, was your sense that Murray brought you over to be the string theorist on the faculty? Was that sort of a niche that you were going to occupy? Had the field been that well developed that you would think about it in terms of faculty lines?
Schwarz:
You know, I think he just heard from these people that this was exciting work and that was good enough for him at that time. But later the issue would arise whether I should stay at Caltech or not. I didn't arrive with tenure, and not everyone was enthusiastic about what I was doing. The position I had when I moved to Caltech was called research associate.
Zierler:
Oh, it wasn’t assistant professor.
Schwarz:
I had been an assistant professor in Princeton for three years.
Zierler:
Right, right.
Schwarz:
The research associate position at Caltech was not the junior post-doc position, which was called a research fellow. It was a senior position. The name was changed several times in the ensuing years, and that position today is called research professor. That sounds much better, but it’s the same position. Research professor is not a tenured position at Caltech, It has to be renewed every five years or so and that depends on funding and satisfactory reviews. I held that position for 12 years before I became a professor. It did have advantages, such as the freedom to do whatever I wanted without any other responsibilities. However, I did volunteer to do some teaching and committee work. Also, I advised lots of graduate students – more than any of the six professors in the group.
Gell-Mann received a nice sum of money from the Fleischman foundation, which he could spend as he saw fit, and he basically used it to bring to Caltech visitors and post-docs of my choosing, which was really great. So in 1974 I arranged for my old friend Joël Scherk, one of the two great French guys that I had met in Princeton, to come to Caltech for half a year. This was the period when string theory had basically just died because of QCD. We were both of the sense that this was a beautiful theory and it ought to be good for something. We couldn't just abandon it.
Zierler:
John, I want to hear about the word beauty, right? Beauty—it’s like you look at a painting. You can see beauty. Where do you see beauty in string theory?
Schwarz:
Well, you know these ideas are subjective.
Zierler:
Of course.
Schwarz:
But string theory has a mathematical coherence, and the more you dig into it, the more you find it’s full of surprises. Anybody who works on it will tell you that. It’s pretty amazing.
Zierler:
So I have to ask then. Maybe it’s--
Schwarz:
It’s not what you put in.
Zierler:
Right.
Schwarz:
It’s not because the people who have invented it are so clever. It’s because the theory is so clever!
Zierler:
Yeah.
Schwarz:
So, for example, today we don't fully understand the resolution of the quantum information problem.
Zierler:
Right.
Schwarz:
But string theory contains the answer, so it’s smart and we haven't yet been smart enough to figure out what it’s trying to tell us. [Laughs] So that’s what I mean by a beautiful theory.
Zierler:
It’s almost a quasi-spiritual question, but if you see the beauty in it, does that mean that you see the truth in it also? Does the beauty convince you of some underlying truth?
Schwarz:
Well, the truth in the particular case that we were addressing in 1974 was that all our attempts to turn this into a theory of hadrons was failing, and now here we have a theory of hadrons, QCD, so is string theory good for anything? One of the problems we faced is that string theory requires massless particles, and the hadron spectrum doesn't have any massless particles.
Zierler:
Why not?
Schwarz:
In particular, one of the massless particles in string theory has two units of spin.
Zierler:
Why does it not have any massless particles?
Schwarz:
The hadron spectrum?
Zierler:
Right.
Schwarz:
Well, the lightest hadron is the pi-meson, whose mass is about 140 MeV. Hadrons are bound states of quarks and gluons. The lightest bound state is the pi-meson.
Zierler:
Okay.
Schwarz:
But string theory requires a massless spin-2 particle. When we tried to get rid of it by fiddling with the theory, it became inconsistent. We knew perfectly well that there is a massless spin-2 particle in nature. It’s the quantum of gravity, a graviton. But that was bizarre, because we weren't looking to say anything about gravity. We were going for the strong nuclear force, so we said, “Gee. Could this particle actually be interpreted as the graviton, and what would that require?”
Well, the first thing it has to require is that the interaction strength should be given by Newton’s constant. When we were thinking of hadrons, the size of the string needed to be the size of a nuclear particle, which is about 10-13 cm, but if you want string theory to give Newton’s constant, the size should be comparable to the Planck length, the length constructed out of Planck’s constant, Newton’s constant, and the speed of light, and that’s 10-33 cm, 20 orders of magnitude smaller. So we could interpret string theory as giving gravity, provided the strings shrank by 20 orders of magnitude, compared to what we had considered previously. It was a rather drastic change in viewpoint.
People who had tried to make a quantum theory of gravity previously would just take Einstein’s general theory of relativity, couple it to other fields, and calculate away, and they would find that perturbation theory doesn't work because you get infinities, ultraviolet divergences, that can't be dealt with by the standard methods of renormalization. This procedure gives what is called a nonrenormalizable theory. However, we knew already from other considerations that string theory does not have those ultraviolet divergences. So we realized that using string theory as a quantum theory of gravity could be very successful.
Zierler:
Meaning it had something to offer even with QCD in mind.
Schwarz:
Yeah. It also gives gauge theory interactions, because there are also massless spin-1 particles. We didn't know how to do it in detail, but it was plausible that you could construct a string vacuum or string solution that describes all of the forces—gravity and all the nuclear and electromagnetic forces all in one go, so it could be a truly unified, consistent quantum theory. So that was the vision, though we were very far from achieving that. To fast forward by 46 years [laughs], we’re still very far from achieving that, but one thing that’s changed in those 46 years is that there are now thousands of clever people who believe it’s possible.
Zierler:
You would think that that number might go in the other direction after 46 years.
Schwarz:
[Laughs] Anyway, when Scherk and I had this realization in ’74 we wrote papers and gave lectures about it, we even submitted a paper to the Gravity Research Foundation’s annual essay competition, which got one of their honorable mentions. I viewed this as a turning point in my life, because this was when I knew what I’d be working on for the rest of my career. That was my feeling.
Zierler:
There wouldn't be another QCD to come along and end that party, you're saying. You were confident of that.
Schwarz:
Yes. I didn't know how far we’d get, but a lot has happened that nobody could have anticipated. I was convinced that this was worth very serious exploration and that’s what I would be doing. Murray Gell-Mann wasn’t an expert on this stuff, but he followed what we were doing, and he took it seriously. So I think it was entirely because of him that I continued to be employed at Caltech for the ensuing decade, because it wasn’t until ten years later that the subject really took off and got widespread recognition. Murray was proud that he believed in protecting endangered species, and at that time he felt that included string theorists.
Zierler:
When did you get tenure?
Schwarz:
at the end of 1984. We can talk more about this later, but in ’84 Michael Green and I had our breakthrough, and then the subject took off.
Zierler:
Right.
Schwarz:
In early ’84 I’d been offered tenure at the University of Chicago and I had decided in my own mind that if Caltech didn't come across, I would move to Chicago. Then Michael and I did this work and Caltech offered me a tenured professorship, and I stayed. So that was another case where things just worked out for me.
Zierler:
How was your work regarded by physicists generally, would you say? I mean, what were some of the basic reactions?
Schwarz:
Are you talking about ’74 or ’84?
Zierler:
No, ’74. We’ll build up to ’84.
Schwarz:
Okay. So in ’74 I think the vast majority were unaware of the work. We gave seminars many places, spoke at conferences, Scherk and I. We were politely received. A few people found this possibility exciting. Names that come to mind besides Gell-Mann would be Lars Brink, Bruno Zumino, David Olive, and a few others. I don't list Edward Witten yet, because he was still too young. He appeared on the scene at the end of the ’70s, so in ’74 he was not yet in the picture. But when he did appear on the scene, he was very supportive.
Zierler:
When you were conveying these ideas at conferences and things like that, what were some of the most important points that you wanted to get across as you were introducing these concepts?
Schwarz:
Well, the basic fact, which I’ve told you already, is that string theory only works if there is a massless spin-2 particle in it. This massless spin-2 particle behaves exactly in the way that Einstein’s general theory of relativity says it should behave at energies low compared to the string scale, which is some absurdly high energy given by the Planck scale, and that string theory incorporates gravity in a framework where the problem of ultraviolet divergences is circumvented, and furthermore that this theory has a rich enough structure that it could describe all of the other forces at the same time.
Of course, we knew the theory requires ten dimensions, and we also knew that the world only has four. [Laughs] We still knew that. So six of the dimensions must curl up somehow to be invisible. Now that didn't make sense when we were trying to make a theory of the strong nuclear force, but it does make sense in the gravitational context. The reason is that in the gravitational context, the geometry of spacetime is determined dynamically. Gravity is a theory of spacetime geometry. So what this theory needs to do is to admit solutions in which six dimensions curl up in a way that they’re small enough that they wouldn't have yet been detected by experiments.
Experimentalists are searching for extra dimensions nowadays. An experimental group at the University of Washington has done Cavendish-like experiments to test Newton’s 1/r2 force law at short distances, and they’ve confirmed it down to the micron scale, which is incredible. This is several orders of magnitude better than had been done previously. This implies that any extra dimensions need to be smaller than that. Also, there’s no sign of extra dimensions from LHC-type experiments, either. But that’s okay. I don't expect them to show up, because my guess is that they’re too small. I could be wrong, of course, so these are important experiments. My guess is that their size is close to the Planck scale, which would make them undetectable. But even if they’re undetectable, they have major experimental consequences, because the details of the geometry of the extra dimensions determine the spectrum and properties of all the ordinary particles that we do observe. So if you found the right geometry for these extra dimensions, you could, at least in principle, derive everything we observe—if this is the right theory, of course.
Zierler:
John, at this period—you know, the mid-1970s going forward—what in the experimental world might you be relying on to advance these theories?
Schwarz:
Yes. Well, one of the frustrating things about working in this subject is that the fundamental scale, which is the string scale, seems likely to be comparable to the Planck scale, which in distance units is 10-33 cm. In energy units, it’s 1019 GeV, which is 16 orders of magnitude beyond the LHC. So it seems unlikely that we’re going to be able to probe such distances or energies in the foreseeable future. If you build a 100-km collider, the next step after the LHC, that gets you one order of magnitude, but we need 16. [Laughs] So it’s hard to see the extra dimensions directly.
It’s hard to think of experimental tests that really probe the guts of this kind of theory, but there are things one can hope for. One possibility is that string theory gives insights into early universe cosmology, some of which might even have observational consequences. There are ideas about gravitational waves that originate in very early universe that might have specific signatures containing useful information. People talk about cosmic strings, which would be defects that you could see in the sky which might somehow be related to fundamental strings. And people are trying to construct specific geometries for the extra dimensions that could lead to realistic particle physics.
One problem is that the solutions of the string theory equations that we understand best mathematically involve supersymmetry, the symmetry that relates bosons and fermions, and observationally there’s no sign of supersymmetry at the LHC or anywhere else. Since we so far don't have the mathematical tools to say anything reliable about non-supersymmetric solutions of string theory, and since the experiments don't show any signs of supersymmetry, there’s a gap that’s preventing us from making a detailed connection.
Zierler:
And that is as true today as it was then.
Schwarz:
Yes. This problem as I’ve stated it is more clearly understood today than it was back then, but that’s the story from the current viewpoint.
Zierler:
Are there technological advances in instrumentation and experimentation that might make the testability more feasible?
Schwarz:
Well, if anyone could think of a way of observing any quantum gravity effect, if there were some signal in the LIGO or EHT data that goes beyond GR, that would be extremely interesting and might have some relevance. Even though there’s a lot of literature on such ideas nowadays, I don't think any of the proposals is terribly convincing. So it’s hard to be optimistic about that. The thing I’m most optimistic about, although somewhat worried, is supersymmetry showing up. When the LHC turned on, most of our community was pretty optimistic that supersymmetry would be discovered at the LHC.
Zierler:
Why? Why the optimism?
Schwarz:
There were several arguments for why the energy scale at which supersymmetry particles would show up would be around 100 GeV to 1 TeV, which is an energy regime that the LHC can explore. So we were optimistic that some of these particles would show up. But none of those arguments is based on string theory and none of them is completely convincing. One of the arguments is something called the hierarchy problem, which I won't try to explain here. Another argument is based on the grand unification idea that you were alluding to earlier. That kind of unification work better with supersymmetry than it does without it. To get it to work with supersymmetry also leads to this particular energy scale, around 1 TeV or so, but with big uncertainties. The uncertainty is always in the exponent, so it’s give or take a factor of 10 or so. And there are some other arguments for why it might be around a TeV. The reach of the LHC will still extend further than it does today after the planned upgrades, so it is possible that supersymmetry will show up.
Zierler:
This is also going to be a little out of chronology, but since we’re talking about the LHC, I’m curious how closely you followed the rise and fall of the SSC and if you thought that some of the work there might be relevant for your theories.
Schwarz:
Sure. The cancellation of the SSC, which was partially constructed, during the Clinton years was a big disappointment for particle physicists. It was going to reach even higher energies than the LHC.
Zierler:
Of course. Right.
Schwarz:
Of course, it would have been at least a decade earlier than the LHC, and in the interim, the technology has advanced. The thing that has advanced most is computers, and even now, the experiments at the LHC are largely limited by computer power because of all the data… To extract the physics information from this data, you need all the computing power you can get. They’re getting deeply into AI and all this stuff to try to process the data. So it’s possible that the SSC might have discovered supersymmetry in the 1990s because it could have gotten to higher energy, but there are a lot of things that the LHC can do today that the SSC couldn't have done back then simply because of advances in computers and magnets and all sorts of other stuff. In any case, it was a tragedy that it was canceled when it was.
Zierler:
Right.
Schwarz:
I think Clinton is on the record as saying it was one of his biggest mistakes.
Zierler:
So let’s build up, then, to 1984. When do you first meet Michael Green?
Schwarz:
So I knew Michael Green in the early ’70s. He had been at the IAS in Princeton when I was at the University—IAS, the Institute for Advanced Study. So I knew him from back then, but we were not close. We never collaborated. We just were acquaintances.
In 1978-79, I spent a sabbatical year in Paris at the École Normale where I worked with Joël Scherk, and following that I spent a month at CERN in the summer of ’79 where I met up with Michael Green in the cafeteria. We got to chatting over coffee about what our interests were. He had worked in the early ’70s on string theory, but had subsequently moved into other areas and was doing other things. But anyway, he knew enough to be on top of things, and one of the discoveries that had come up…in 1976 …was the realization that this 10-dimensional string theory ought to have spacetime supersymmetry. We knew since 1971 that it had world-sheet supersymmetry, but let me explain these terms.
A string is a one-dimensional extended object. It sweeps out a two-dimensional surface in spacetime, if you follow its time evolution. Just as a point particle sweeps out a line in spacetime, a string sweeps out a two-dimensional surface in spacetime called the worldsheet of the string. One can formulate string theory in terms of the physics of that two-dimensional surface. We knew since 1971 that the theory on that two-dimensional worldsheet has supersymmetry properties, but what wasn’t known in the early ’70s was that string theory has ten-dimensional spacetime supersymmetry. So the physical spectrum of particles in ten dimensional Minkowski spacetime should have Bose-Fermi symmetry.
This had been discovered by Gliozzi, Scherk, and Olive in ’76. The evidence they gave was that at every mass level in the spectrum of the string, there is an equal number of bosons and fermions. This is a necessary consequence of supersymmetry, but not a proof that you actually have supersymmetry. So I wanted to prove that it was really there, and I suggested… [Laughing] When we were chatting in the cafeteria, I suggested to Mike that we try to prove it.
To make a long story short, we did prove it, but it took a couple of years. We had a very intense collaboration for about six years. Well, seven years if you include writing our textbook. During that period we collaborated every summer at the Aspen Center for Physics, and Mike had extended visits at Caltech on several occasions, and I had one extended visit in London. In those days he was at Queen Mary University in London. So that’s how our collaboration began.
Zierler:
The breakthrough—how did you know when it happened?
Schwarz:
Yes. Well, we were very excited when it happened! [Laughs]
Zierler:
Was it a slow build or was it really like a eureka kind of moment?
Schwarz:
It was a eureka moment (my second one). One of the features of the real world is that it has what’s known as parity violation; this is a feature of the weak nuclear force. What this means is that if you take a movie of some physical process and you turn the film over so you play it side-reversed and you exchange left and right, you can see that it violates the laws of physics. [Laughs] The laws of physics prefer one-handedness to the other. So that’s called parity violation and it’s a feature of the weak nuclear force.
So if string theory is to give a consistent, unified theory, it should be able to account for parity violation, in particular. The problem with parity violation is that typically, if you try to write down a relativistic quantum theory with parity violation, it leads to inconsistencies. It could be a consistent classical theory, but it could turn out to be inconsistent as a quantum theory. The inconsistency is given by something called anomalies, and basically these anomalies imply that the gauge symmetry that makes the classical theory consistent is broken by quantum corrections. So the question arose: does string theory have parity-violating solutions that don't have anomalies so that there is a consistent parity-violating quantum theory?
Well, in ten dimensions, Michael and I had formulated (and named) three different superstring theories, which we called type I, type IIA, and type IIB. The type I and type IIB theories have parity violation and the type IIA does not. In 1983, Luis Alvarez-Gaumé and Ed Witten proved that the anomalies cancel in the type IIB theory. This was something I expected to happen, but I hadn't proven it. But in the 1980s there was no idea how to get anything realistic out of the type IIB theory. The type I theory at the time was regarded as the best prospect for getting out realistic physics, and so the question was whether the type I theory has anomalies or not.
Now the type I theory was not a unique theory because there was a gauge symmetry that you could associate to it which could be given either by an orthogonal group or a symplectic group. There is an infinite family of orthogonal groups and an infinite family of symplectic groups. So classically it was really two times an infinite number of theories.
So what we needed to do was to compute the anomaly of the type I theory and see whether or not it vanishes. As a string theory calculation, there were two diagrams we had to combine, which I alluded to earlier. One is a cylinder and the other is a Möbius strip. So we computed the anomaly associated with each of these. This was in the summer of ’84 when we were in Aspen. I was the organizer of another workshop there that summer. By then there was interest in extra dimensions by other theorists, who were not yet interested in string theory, and so I organized a workshop on the physics of higher dimensions. That brought people with related interests to the Aspen Center for Physics. This was fortunate, because discussions with some of them were quite helpful.
Zierler:
Such as what? What are some related interests?
Schwarz:
Well, there was something called 11-dimensional supergravity, which is a classical theory in 11 dimensions, and there were studies on how to compactify 7 of the 11 dimensions to get interesting physics in 4 dimensions. That wasn’t string theory, but it was interesting and involved many related concepts, which later would be understood to be even more deeply related to string theory than we knew at the time.
Once, when we were walking to a seminar during this workshop, I said to Mike “Maybe there is a particular gauge group for which the contributions of the cylinder and the Möbius strip cancel.” At the end of the seminar, Mike comes up to me and says, “SO(32),” [chuckles] which was the correct answer. Among these two times infinity possible gauge groups, only that one, an orthogonal group in 32 dimensions, would lead to anomaly cancellation for the type I superstring theory. For any other choice it is not a consistent quantum theory.
That was not the first work we published on anomalies, however, so we held on to it. First, we wanted to understand better what was going on by looking at a low-energy effective field theory analysis. In that setting, we could study the gravitational anomalies as well as gauge theory anomalies. The string theory computation we had done only checked that the gauge anomalies cancel, but there were also gravitational and mixed anomalies one should worry about. From the effective field theory viewpoint, we got a deeper understanding of what was going on and showed that many additional miracles were taking place for SO(32) in the type I string theory such that all of the relevant anomalies would cancel and you’d have a consistent quantum superstring theory with parity violation.
By then Witten was a highly influential fellow. He was not in Aspen that summer, but word got back to him at Princeton about our work. (This was pre-Internet.) So I got a call from Edward. “I hear you’ve made some progress on the anomaly problem,” and I said, “Yes. Mike and I are just working on a paper.” So he said, “Can you send me a copy of your draft?” [Chuckles] So we had this unpolished and incomplete manuscript… It wasn’t even a preprint yet; it was a pre-preprint [laughs] which we FedExed (the fastest available communication other than phone) to Edward.
Zierler:
[Laughs] Did you have a sense of what Witten was working on at the time that he made contact with you?
Schwarz:
He was working on a lot of things. The guy’s incredible.
Zierler:
Yeah.
Schwarz:
I think after he got our paper it probably took him a microsecond to understand it. [Laughter] The greatest conglomeration of experts was to be found in the Princeton area between the University and the Institute, and I am told that within a matter of days they were all working on this stuff. [Laughs]
Zierler:
Oh, wow. Because of Witten? Witten spread the word?
Schwarz:
Absolutely. Yeah, absolutely. He was the pope. [Laughs] I just read a biography of Enrico Fermi, which is entitled The Pope of Physics. [Laughter] So that’s what put that word into my head.
Zierler:
[Laughs] Although for Witten, maybe more appropriately – he was the rebbe of physics or something like that. [Laughter]
Schwarz:
By the way, my relation to Enrico Fermi is that Geoff Chew was Fermi’s student.
Zierler:
Right.
Schwarz:
So I’m a Fermi grand-student.
Zierler:
Right, right. So in what ways and how quickly did Witten really substantively contribute to this work?
Schwarz:
So he wrote a short letter which appeared soon after ours, where he made a few observations which were nice, but none of them I think was earth-shattering. But it showed that he fully understood our work and was advancing the subject. But then a few months later, he had a paper with Philip Candelas, Gary Horowitz, and Andrew Strominger, which is a very famous paper. It identified a class of six-dimensional geometries that were particularly promising choices for the extra dimensions. These were the kinds of geometries that had been studied by the mathematicians Calabi and Yau. So they called these geometries Calabi-Yau spaces. They argued that if you take certain string theories and compactify them so that six dimensions form a Calabi-Yau space, this would be a consistent thing to do because it has certain technical properties such as Ricci flatness. Moreover, this would preserve just the amount of supersymmetry that we were hoping to find in four dimensions, called N = 1 supersymmetry, which is what experiments look for. They didn't have a specific example that was fully realistic because there are a very large number of Calabi-Yau spaces and it was not clear which is the right one or even whether there is a right one. But in any case, this demonstrated that it is possible to come quite close to getting realistic physics by choosing the extra dimensions to be a Calabi-Yau space. This Candelas, Horowitz, Strominger, and Witten paper was extremely influential, and it initiated a program that is still very active 35 years later.
Zierler:
At the Institute.
Schwarz:
Everywhere.
Zierler:
Everywhere?
Schwarz:
Worldwide.
Zierler:
In what ways did Witten advance with his collaborators the theories that you had worked on up to that point?
Schwarz:
To answer you I need to back up a bit. What I failed to mention was that there was another important paper that appeared a bit earlier by Gross, Harvey, Martinec, and Rohm. It introduced what they called a heterotic string. I mentioned the three superstring theories that Michael and I found (the type I, IIA, and IIB) and it turned out that there were two more string theories which these people discovered. One heterotic theory uses the group SO(32) again and the other one which uses another group called E8 × E8. E8 is the largest of the five exceptional Lie groups in the Cartan classification. In the Candelas, Horowitz, Strominger, Witten program, the example that looked most promising for getting realistic physics was based on the E8 × E8 heterotic string, so it wasn’t actually any of our three theories that people were excited about at this point, but rather the E8 × E8 heterotic string theory.
Michael and I had observed from the low-energy analysis in our original paper that E8 × E8 is another group that could be consistent with anomaly cancellation, but we hadn't yet formulated a string theory based on E8 × E8. These people beat us to it.
Zierler:
John, as a result of these advances in 1984 and 1985, how did the basic research questions change, the kinds of things that you were asking from 1974 and then through the next decade? And then how did your research focus and the kinds of questions you were asking change as a result of these advances?
Schwarz:
So the big change was that instead of three or four people working in the subject, it quickly became hundreds… I mean, last week was the Strings 2020 conference.
Zierler:
Right.
Schwarz:
It was supposed to be in Cape Town, but due to the pandemic it was on Zoom, and there were 2,700 registered participants. [Laughs]
Zierler:
Amazing. Amazing. How variegated is the research? Is everybody asking basically the same fundamental questions and it requires this much labor to answer them, or are there many branches that have sort of been borne out over the years?
Schwarz:
It’s definitely the latter—all sorts of different topics, some of which don't even sound like string theory, that people are working on but are related one way or another to this general program. A lot of the discussion this year focused on the problem of quantum information associated with black holes. One of the big puzzles that Hawking recognized in 1976 was that a fundamental problem in reconciling general relativity with quantum theory is that is if you form a black hole starting from a pure quantum state, by the time the black hole evaporates by giving off Hawking radiation, which is what happens over a long period of time, it appears that you would end up with a mixed quantum state. That would be a violation of quantum theory because unitary evolution doesn't allow a pure state to turn into a mixed state. Hawking concluded that quantum theory must break down. The current consensus is that there definitely must be unitary evolution, and quantum theory is sacrosanct. Almost every expert in the world is convinced of that. Eventually, before he died, even Hawking became convinced of that. He held out until a few years ago, but he agreed finally that there must be unitary evolution. But it is really hard to explain in detail how that works. This gets back to what I was saying earlier that string theory is smarter than we are, because I’m convinced it contains the answer, but we haven’t yet figured out how to extract it.
Zierler:
What is the answer, John?
Schwarz:
Well, I mean string theory gives black holes and it gives unitary evolution, so it has to work! But to explain in detail what was wrong with Hawking’s argument is really hard. So a significant fraction of this year’s conference was addressed to that question. There are no final answers, but there is a lot of progress.
Zierler:
What do you think mostly accounts for this progress? Is it just more really smart people working on these questions? Is it advances in cosmology, advances in computing? What are the factors that account for these advances?
Schwarz:
Since the mid-’80s, there have been two major, major developments in the field which really ought to be mentioned. The first was in the mid-’90s when we started to understand aspects of string theory that went beyond perturbation theory. So for example, there was a feature called S duality which is something that relates one string theory at weak coupling to another string theory at strong coupling with g as the coupling constant of one theory, and 1/g as the coupling constant of the other theory. This kind of relation is great because it means that if you can compute one of them for small g, you know the other one for large g. This kind of relationship occurs between the SO(32) heterotic string and the type I SO(32) string. They’re related by S duality. And it turns out the type IIB string is related to itself by S duality. So that was discovered in ’94, ’95. There were generalizations of that due to Hull and Townsend in Britain, and Witten made major contributions as well to non-perturbative aspects of string theory that the string theory community started to understand in the mid-’90s. So that period is sometimes referred to as the second superstring revolution.
Zierler:
Mm-hmm [yes], and even more people--
Schwarz:
I actually introduced that term because in ’95 when I was invited to give a lecture at a conference in Moscow, where I described these recent developments, I gave as the title of my talk “The Second Superstring Revolution”. One of the participants came up to me afterwards and said, “You know, we really don't like revolutions.” [Laughter]
Zierler:
John, I’m curious if you can talk a little bit about how you regard some of the basic criticisms of string theory. In other words, one of the common ones is that it’s not testable. My first question is do you just reject the premise of that criticism, or would your response be, “It’s not testable yet”?
Schwarz:
Well, let me answer in a broader framework.
Zierler:
Please.
Schwarz:
So there have been many criticisms of string theory over the years, and they were particularly intense in the period from ’85 to ’95. In the first decade after it took off there was a lot of criticism. In fact, I was astonished to learn that my name had been suggested to you by Shelly, because he was the most outspoken critic of all. [Laughs] Perhaps he was trying to atone for that. [Laughter]
Zierler:
May be!
Schwarz:
Anyway, he’s a nice guy. I like him, regardless. But some of the criticisms made sense and were based on good physical reasons like you were alluding to and some of them were based on pure prejudice and ignorance and can be dismissed as such.
One in the first category, the one that was well-founded, in that category I’d put Richard Feynman. I discussed it with him quite a bit after the anomaly cancellation result. He was very curious about it. There was a book that came out in ’85 or ’86 based on interviews done for a BBC radio program, and there was one chapter for each of the people they talked to. One of them was Richard and he was asked what he thought of string theory, which was the subject of the book. He had a beautiful way of responding. He said, “When I was a young physicist, I observed that whenever an exciting new idea would come along, the older physicists would be very dismissive of it and very skeptical. Now I’m an older physicist and these exciting new ideas have come along and it would be very easy for me to make the same mistake.” Then he went on and he said, “Well, I’m going to do it anyway!” which is typical Feynman charm.
The basis for his concern is perfectly understandable, that it was so far removed from anything that we can think of observing experimentally that is it physics? I don't think it was obvious at that time whether it was just some branch of mathematics or whether it’s physics. [Laughs] Now I think we know much more today. We haven't experimentally confirmed string theory, but a lot has happened which is very exciting.
First of all, it’s had a profound effect on fundamental mathematics. A significant fraction of modern mathematics has been motivated by developments in string theory. In fact, Witten was a winner of the Fields Medal for his mathematical contributions. He and others have made enormous contributions to mathematics. The fact that this theory is deep enough that it can have that kind of impact shows there’s something very nontrivial there in many different branches of mathematics, which is exciting because it implies connections the mathematicians might not have otherwise anticipated. Mathematicians are always looking for connections between different areas of mathematics so they can transfer the results from one area into another and unify them, and string theory gives hints about that. There’s something called the Langlands program which is a dramatic example of that in mathematics, and Witten with two of my Caltech colleagues has made important contributions to that program, partly motivated by developments in string theory.
So that’s one thing. You could say, “Okay, that’s just math.” However, the mathematical tools that we’ve developed (the string community, not me) turn out to be useful in other areas of physics. So one of the exciting developments I was going to mention earlier and then forgot or didn't get to was that in 1997 there was this fantastic breakthrough by Juan Maldacena which relates gravity theories to gauge theories in special situations. Sometimes this goes by the name of AdS/CFT. AdS stands for Anti-de-Sitter space. This is a negatively curved solution of Einstein equations for spacetime, and CFT stands for conformal field theory. Conformal field theories are a special class of field theories which have conformal symmetry, which is an extension of Poincaré symmetry, which is the usual relativistic symmetry in quantum field theory. Maldacena’s discovery that there is this connection between string theory in anti-de-Sitter space and conformally invariant field theories was a major breakthrough.
In fact, one of the specific examples he gave I’m very proud of. Even though he didn't reference either of them, both sides corresponded to theories that I had co-discovered. One is N=4 super Yang-Mills theory with an SU(N) gauge group, which I had introduced with Lars Brink and Joël Scherk, and the other is type IIB superstring theory in an AdS5 × S5 geometry with N units of five-form flux. So his speculation, which he gave good evidence for, was the equivalence of these two very different-looking theories. This paper by Juan, by the way, is the most highly cited paper in theoretical physics ever, or at least since the Internet. A couple of years ago it passed Weinberg’s Standard Model paper in citations. [Laughs]
Zierler:
That’s pretty good company!
Schwarz:
So that work from ’97 is still a major theme in theoretical physics, and it shows that string theory and quantum field theory aren’t as unconnected as I might have thought earlier. In special situations, at least, string theory is equivalent to quantum field theory. So that’s a major theme that people have been studying in recent years. This AdS/CFT correspondence provides tools for studying features of conformal field theories at strong coupling. The reason is that when the conformal field theory is strongly coupled the dual string theory is weakly coupled, and vice versa. This is like the S dualities I was talking about before. You can compute weak coupling, by using perturbation theory. So by doing weak coupling calculations in a gravity theory, one can say things about conformal field theories at strong coupling, and strongly coupled conformal field theories pop up in condensed matter physics all over the place.
Zierler:
Mm-hmm [yes].
Schwarz:
Many of the younger condensed matter physicists who are amenable to new ideas [chuckles]—plus a couple of the older ones who are also amenable to new ideas—have been actively pursuing the application of these tools in their field. So that’s an example of the kind of spinoffs that have been coming. There are other areas of physics, including nuclear physics, where there are similar developments. Condensed matter is perhaps the best example.
Zierler:
So it sounds, John, like in some ways string theory today is as exciting as it was in 1974 or 1984.
Schwarz:
Well, in ’74 it was a community of a few hundred people.
Zierler:
Right.
Schwarz:
By the mid-’80s, it may have been 1,000 or so, and by now it’s probably closer to 5,000. These numbers are necessarily imprecise.
Zierler:
And in terms of distribution, you know, in terms of the physics community broadly voting with its feet, how well represented are string theories on academic campuses—not just in the United States, but worldwide?
Schwarz:
Well, it is worldwide.
Zierler:
As far as you're concerned, are things moving in the right direction, you know, from a so-called campaign to keep certain faculties string-free, right? Where are we today on that?
Schwarz:
I think this was an issue maybe from ’85 to ’95 or so, and maybe even longer in some places, but by now it’s no longer an issue. Any place that wants to get into fundamental theoretical physics has a presence in this field. I think the fact that you got my name from Shelly speaks more loudly to this than anything I can think of. [Laughs] Because he was really an extreme example. There were a couple popular books that attacked string theory about a decade or so ago. The authors clearly had chips on their shoulders. For people without a physics background it’s not possible to assess whether what they’re reading makes sense or not. But anyone with at least an undergraduate education in physics I think can recognize that they should not be taken seriously.
Zierler:
John, this idea that you shared with me that string theory in some ways is smarter than the people who are working on it, right?
Schwarz:
Yes.
Zierler:
So I wonder, then. Does that sort of presuppose that string theory by definition really can't be testable until it’s understood? In other words, don't you need to truly understand the theory to know what it is that you're testing for?
Schwarz:
Well, we understand it in various limits, but we don't have a full understanding. We don’t know whether there is a more fundamental description of the theory than what we already have. My guess is that there is one. As I said, we can calculate at weak coupling and at strong coupling, but what about in between? [Laughs] So there are gaps in our understanding. I also mentioned that we understand how to get solutions with supersymmetry in four dimensions, but we don't have any convincing ways of understanding non-supersymmetric theories in four dimensions.
Then there’s another big question. We know observationally that there’s what’s called dark energy in the universe, and the best guess for dark energy is that it corresponds to a cosmological constant. This is something that Einstein introduced early on in his work and then renounced as a mistake; but it wasn’t stupid, it was very smart. Observationally it appears that there is a small positive cosmological constant, and that’s the simplest guess for what dark energy is. But one thing we know is that a positive cosmological constant is inconsistent with supersymmetry. We can easily write down supersymmetric solutions with a negative cosmological constant. That’s how you get anti-de-Sitter space, but not with a positive cosmological constant. So there’s a real question whether string theory has solutions that give a positive cosmological constant. There was some work some 10 or 15 years ago by Kachru, Kallosh, Linde, and Trivedi proposing a mechanism to obtain such solutions. It’s not clear whether that work is correct or not. There’s a lot of discussion back and forth on that, and I don't have an opinion. But it’s conceivable that any solution with a positive cosmological constant is unstable, which would mean imply that the universe would decay into some other situation either by rolling down a potential (this goes by the name of quintessence) or by going through a quantum barrier, which could introduce frightening possibilities for the future. These are deep questions for which people would love to understand the answers. As we understand string theory better, I think questions like this might be answered someday without requiring any new experimental advances. On the other hand, at a much more down to earth level, if supersymmetry were discovered at the LHC, that would be super important from several viewpoints.
Zierler:
And you think it could happen at CERN? We’re not waiting for an ILC kind of creation?
Schwarz:
An ILC or a next proton collider. Well, there’s no guarantee, and the fact that it hasn’t shown up yet is worrisome.
Zierler:
Right. Right.
Schwarz:
I’m not saying that it will happen, but I’m just saying it could happen and that would be really exciting for several reasons. One is it would set the experimental agenda for the remainder of the century. Otherwise, there’s a danger that experimental high energy physics could die.
Zierler:
Right.
Schwarz:
and that the next-generation colliders might not be built, that the expertise that’s been developed would be lost and be really hard to regain. I think that would be extremely sad. And the discovery of supersymmetry, I am convinced, would ensure that that doesn't happen. So that’s one aspect of it. The other aspect of it is we would be forced to invent a new standard model which would extend the current standard model to something better. It would still be some quantum field theory. It wouldn't be string theory. It would be some quantum field theory which incorporated whatever the new physics is that was discovered. That would be important because it would… For people who are working from top-down, it would give a better target to aim for. It’s really hard to connect our lofty ideas in ten dimensions down to the existing Standard Model, but if we know something that’s a little better than the Standard Model, with a higher level of unification than we have now, that should give us an easier target to shoot for and would be enormously useful guidance in developing theory.
The discovery or non-discovery of supersymmetry would not prove that string theory was right or wrong, but its discovery would be very encouraging. String theory requires supersymmetry, but it doesn't tell you what energy scale it should appear at. All the arguments that specify an energy scale that I referred to earlier are not based on string theory. As far as our current understanding of string theory is concerned, the supersymmetry scale could be anywhere up to the Planck scale. But I’m convinced that at sufficiently high energy there is supersymmetry. I’m utterly convinced of that, but I don't know at what energy it starts to show up. It might be beyond our technological grasp.
Zierler:
John, another way of assessing criticism of string theory… You know, in one way you can isolate string theory and say it’s not testable, but another way of getting at that question is to assess in what ways string theory has influenced other fields in physics, whether they know it or not. In what ways has the work that you’ve been involved with advanced superconductivity or condensed matter or particle physics or cosmology, right? Where do we see the fingerprints of string theory in other areas of physics, even if they don't even understand or appreciate it?
Schwarz:
Sure. Well, I already mentioned about AdS/CFT’s impact on condensed matter physics…
Zierler:
Right.
Schwarz:
which is perhaps the outstanding example of what you're asking. But there are certainly other examples. There are conferences on string cosmology. I’ve never attended any of them. [Chuckles]
Zierler:
Are you not personally interested?
Schwarz:
I haven't tried to become an expert on cosmology. I follow it at a distance. I know the basic ideas, but I’m not fluent in the details. But it is definitely a setting in which it is conceivable that string theory could be tested. I’m not saying it will happen, but I’m saying it might happen. Some of the ideas that are being proposed in cosmology are motivated by string theory. For example, the idea of inflation did not arise out of string theory; that’s been developed independent of string theory, and inflationary cosmology is widely believed, though not universally, to be basically in outline correct. But there are lots of details to be filled in which include what kinds of particles or fields are involved and what kinds of interactions they have. Many people who work on those questions are motivated by string theory considerations. So cosmology is a general area in which it’s conceivable that string theory will have an impact or be illuminated.
Zierler:
What about multiverses? String theory has a lot to say about multiverses.
Schwarz:
Yeah. It’s a subject that I’m uncomfortable talking about because I don't feel I understand it very well. So I won't. [Laughs] What I can say is that superstring theory has many different solutions, and the Universe we inhabit presumably corresponds to one of them. If other solutions also arise somehow, somewhere, I couldn’t say.
Zierler:
You're just not one of them.
Schwarz:
No. [Laughter] I went to a colloquium once—I guess it was by Kachru—entitled “The Theory of More Than Everything.” [Laughter]
Zierler:
That’s great!
Schwarz:
That was about the multiverse.
Zierler:
John, have your own questions changed over the years? Are there bedrock questions that you’ve been asking for 40 years or so that remain the same, or have some of your fundamental questions changed over the years?
Schwarz:
Well, I think the questions I was worried about in the ’70s and ’80s have been largely answered, and the questions that one can dream about like how do we connect to the real world are out there, but I don't have anything particularly wise to say about them except in general terms like I’ve been attempting with our discussion. [Chuckles]
One detail I meant to mention earlier is that in trying to connect string theory to potentially realistic models, I had earlier said that the type IIB superstring doesn't work. That was true as long as we only understood perturbation theory. But when we go beyond perturbation theory, there is a way of approaching type IIB string theory developed by Cumrun Vafa from Harvard, which he named F-theory. Why he called it F-theory doesn’t matter, but anyway, he called it F-theory. It is a method for constructing non-perturbative solutions of type IIB superstring theory. F theory currently appears to be a promising approach to getting quite realistic solutions. So that is a very active area of research. It’s not research I’ve engaged in myself. It involves very fancy mathematics, which I’m too old to absorb, but it’s certainly great work.
Zierler:
John, now that we have thousands of string theorists working on these issues today, many of whom are young—they will be working on these for decades to come, and as you emphasize now, they’re all working in sort of different branches of string theory—what do you see as the most promising work now that’s being done, perhaps by the next generation of string theorists? What are the questions that they’re seeking to answer, and what is your overall assessment of that?
Schwarz:
Yeah, okay. Well, if I look at the Strings 2020 conference, which was last week, there were three or four talks that particularly seemed to me to be pointing in interesting directions. The one by Cumrun Vafa I found fascinating. By the way, these talks are all archived on the Internet. Vafa and Hirosi Ooguri and others are trying to determine the general features that can occur in string theory solutions and the features that never occur. The ones that are allowed form what they call the string landscape, and the ones that are forbidden they call the swampland. It sounds like silly jargon, but they’ve actually made a lot of progress in delineating these two broad categories. There are certain properties of black holes and other things that are strongly influenced by these results, the swampland program.
Vafa put forward an idea in his talk that he called the string lamppost principle. I hadn't heard it explicitly stated before, but it was one of these cases of love at first sight. He speculated that any quantum mechanically consistent way of combining ordinary forces with gravity necessarily will arise as a solution of string theory, and he gave some evidence for this. It’s far from a proved theorem, but I think it’s an interesting direction to think about. If it were true, it might raise the question, what are all these people who claim they have other ways of approaching quantum gravity actually doing? [Laughter] So that was one talk that caught my interest.
Another interesting talk was given by Clay Cordova a young fellow, also at Harvard. Clay talked about higher symmetries, a subject that has taken off in the last couple of years. Ordinary symmetries are associated with point particles and higher symmetries are associated to higher dimensional objects. We’re familiar with gauge symmetries and global symmetries in quantum field theory. Those are all point particle concepts, and it turns out that these higher symmetries, which can also be global or local, appear in all sorts of places one might not have anticipated. It seems that there is a lot to be learned from a more complete understanding of these symmetries. Just as the ordinary symmetries can have anomalies which can either make a theory inconsistent when they’re associated to local symmetries or can tell us important features of a theory when they’re associated to global symmetries, the same is true for these higher symmetries. This is a subject that’s just started to be explored in the last couple of years, and it’s deeply tied up with string theory. As we develop a better understanding of higher symmetries, I’m convinced this will lead to a lot of progress.
There were a lot of talks about the black hole information paradox, and Maldacena gave a very nice overview of the recent progress in addressing that problem. The bottom line is that in very unrealistic situations, several groups have proved that there is unitary evolution of black holes, but it’s still a major challenge to extend this to more realistic situations. So those are a few of the current directions.
Zierler:
How far away can string theory move from experimentation and still move the field forward?
Schwarz:
As I said, if supersymmetry is not discovered, there’s a danger that experimental particle physics will die. If that happens, it would be tragic, but it wouldn't be the end of string theory. String theory will continue, regardless, and will continue to advance. But we definitely need more experimental guidance to tell us what to look for.
Zierler:
Because it will advance much more productively if it is found.
Schwarz:
If any new physics turns up, that will give us something to try to explain and that will be very helpful. I still think that supersymmetry is the most likely possibility.
Zierler:
In what ways might string theory contribute to our understanding of t = 0 right at the very beginning?
Schwarz:
Well, there is a lot of literature on the early universe. Some are using string theory; some are not using string theory. In the not-string-theory setting, there are some ideas due to Hartle and Hawking which are very influential about the origin of the universe, which I don't fully understand. It’s conceivable that somebody will come up with a nice string theory explanation of how the Universe started, but I don't know. [Laughs] It’s not something I’m trying to do.
Zierler:
John, can you say something about the string theory books you have written?
Schwarz:
I’ve coauthored two string theory textbooks. The first, coauthored with Green and Witten, is a two-volume work that was published in 1987. This was the first thing any of us wrote using TeX, and it was the first book that Cambridge University Press published from camera-ready copy. The internet was not yet in wide use, so we exchanged files using capabilities set up by our experimental colleagues. Another obstacle was that computers were very slow back then, and it took a long time to process a chapter. We worked like crazy, and wrote the whole thing in nine months. I think these books have been helpful for people entering the field.
The second string theory textbook was coauthored with Katrin Becker and Melanie Becker, sisters who had been postdocs in our group at Caltech. It was entitled “String Theory and M-Theory, a Modern Introduction.” It was published by Cambridge University Press in 2007. It contains a lot of material that originated during the intervening 20 years. I have also coauthored a textbook on special relativity with my wife, Patricia Schwarz.
Zierler:
Well, John, I think for my last question I want to ask-- You know, we’ve been talking about the field generally for even this past portion of our discussion. What motivates you personally? What are the contributions that you want to make? What are the issues that continue to be of most interest to you and that you want to work on yourself?
Schwarz:
Well, I’m realistic about recognizing that my best years are behind me. I’m 78 now and retired, and I don't feel driven like I used to be. I don't feel I have to prove myself. [Chuckles] But I do want to try to keep abreast of what’s going on, and maybe I can still make some contributions.
Zierler:
But John, if I may, there are two functions of that probably. One might be age, but two might be that you feel vindicated for what you’ve contributed so far.
Schwarz:
Well, sure. Yes, I’m very happy with how things worked out. [Laughs] What might have turned out to have been a kooky idea wasn’t after all. [Laughter]
Zierler:
I wonder if…
Schwarz:
So it’s possible I’ll make some minor contributions in the future, but I don't expect to make any significant breakthroughs.
Zierler:
Are you in contact with younger generations who might ask for advice on things that they should work on?
Schwarz:
Not as much as I would like. The pandemic is not very good that way.
Zierler:
Right.
Schwarz:
But even before that, I mean we have a great group of post-docs at Caltech. I go to their seminars and I’m aware of what they’re doing. Occasionally I talk with them, but in recent years I haven't been interacting a lot with them or with the students. My last student graduated a year ago. At the moment I’m not in the midst of any collaborations. There are a few items on my ideas-to-explore list, but I keep finding that I have more urgent things to deal with.
Zierler:
[Chuckles] Well, it’s another reason to look forward to the end of coronavirus pandemic, right?
Schwarz:
Right.
Zierler:
Well, John, it’s been a delight talking with you. I really appreciate this time we spent together.
Schwarz:
Thank you, David.
Zierler:
Okay.