Juan Maldacena

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ORAL HISTORIES
Image of Juan Maldacena

Credit: Andrea Kane, Institute for Advanced Study

Interviewed by
David Zierler
Interview date
Location
Video conference
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Interview of Juan Maldacena by David Zierler on January 15, 2021,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
www.aip.org/history-programs/niels-bohr-library/oral-histories/47184

For multiple citations, "AIP" is the preferred abbreviation for the location.

Interview with Juan Maldacena, Carl P. Feinberg Professor at the Institute for Advanced Study. Maldacena recounts his childhood in Buenos Aires, he discusses his undergraduate education at the University of Buenos Aires and his advanced work in physics at Instituto Balseiro where he had his initial exposure to string theory. He explains his decision to pursue a graduate degree at Princeton where he worked with Curt Callan and where he benefited from Ed Witten’s lectures on dualities in quantum field theory and in string theory. Maldacena describes his thesis research on conformal field theories with boundaries and the significance of Joe Polchinski’s discovery of D-branes, and he conveys the importance of his collaboration with Andy Strominger as a postdoctoral researcher at Rutgers. He describes his paper on AdS/CFT while at Harvard and he explains his work on non-gaussianities and his realization that string theory would be useful for cosmology. Maldacena explains his decision to leave the faculty at Harvard to join the Institute, and he describes his subsequent research on space-time and entanglement, the chaos of black holes and the likelihood that they are rapidly thermalizing systems. He explains the contributions of string theory research as offering physics a model for quantum gravity and for the quantum mechanics of spacetime itself, and he shares his perspective on broader debates about how many researchers should or should not be involved in string theory work. At the end of the interview, Maldacena describes his hope in the future to better understand the interiors of black holes.

Transcript

Zierler:

Okay. This is David Zierler, oral historian for the American Institute of Physics. It is January 15th, 2021. I'm delighted to be here with Doctor Juan Martín Maldacena. Juan, it's great to see you. Thank you so much for joining me.

Maldacena:

Yes, it is nice to see you too.

Zierler:

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

Maldacena:

I am the Carl P. Feinberg Professor at the Institute for Advanced Study.

Zierler:

Now, the Feinberg endowment was a recent development. Do you have any particular connection to the Feinberg family, or was he particularly interested in supporting your work?

Maldacena:

I met Carl about ten years ago. He is a software entrepreneur, and he has been very interested in physics, following the work in our field. I guess he was interested in funding me.

Zierler:

Juan, I'd like to ask a very in-the-moment question before we go back and trace the narrative of your life and your background. And that is, a caricature of theorists, of course, is that they like nothing better than to be left alone in a room with their pen and their paper doing their calculations, and so the assumption is, this has been an ideal time of productivity during the pandemic and the mandates of physical distancing. To what extent has that been true for you? In other words, have you been especially productive during this time? Or alternatively, what has been missing for you in terms of being able to collaborate and seeing your colleagues not just on Zoom?

Maldacena:

Actually, a lot of new ideas arise when we talk to other people. Of course, we can talk by via Zoom, but it is better when we talk in person. But I used my time to do some projects that I wanted to do which are a bit off the beaten track.

Zierler:

So, what have you been working on recently? What have you been doing over the past year?

Maldacena:

These projects involved aspects of magnetic black holes and also wormholes that are big enough to allow for a person to travel through them.

Zierler:

These are topics that you might not necessarily have pursued under more normal circumstances?

Maldacena:

Probably not.

Zierler:

Well, Juan, let's take it all the way back to the beginning. Let's go back to Argentina. Tell me first about your parents. A little bit about them and where they're from.

Maldacena:

Both of my parents are from Argentina. My father is an engineer, and had a company installing and servicing elevators. My mother is a public English translator. While we were young, she stayed at home. After we grew up, she started working with my father, importing elevator parts.

Zierler:

How many generations back does your family go in Argentina?

Maldacena:

Basically one, their parents are from Italy or Spain.

Zierler:

Now, based on EU laws, do you have nationality or citizenship that can go back to Italy or Spain?

Maldacena:

Yes, I have the Italian citizenship.

Zierler:

And where did you grow up? What neighborhood in Buenos Aires did you grow up in?

Maldacena:

I grew up in a middle-class neighborhood called Caballito, on the ninth floor of an apartment building.

Zierler:

And what kind of schools did you go to growing up?

Maldacena:

For elementary school, I went to a private Catholic school called La Salle. Then for high school I went to a military school, the Liceo Militar General San Martin.

Zierler:

Was the Catholic church a big part of your childhood?

Maldacena:

Yes, and I am still a church goer.

Zierler:

Juan, you grew up during a very tumultuous time in Argentinian history in the 1970s.

Maldacena:

Yes.

Zierler:

Did that affect you or your family personally? Did you see these things happen in your own life?

Maldacena:

It was a time of fear in the family. We were afraid of communists. I remember there was a bomb that went off in the building across the street from our apartment, leaving a big hole in the wall. The apartment belonged to a university dean. A student had befriended his daughter and put a bomb under his bed. Fortunately, the dean was not there at the time, so he didn’t die.

Zierler:

Juan, what were the decisions that you or your family made for you to attend a military school?

Maldacena:

I went because my uncle had gone to this military school. It was a good school academically, and it was supposed to be good for your character (laughter). I think it was not a particularly good fit for my interests.

Zierler:

Juan, when did you start to get interested in math and science? Was it early on?

Maldacena:

There was an entrance exam to this military school, and I went to an academy to prepare for it. I was particularly interested in the math side and the teacher gave me interesting side problems. During high school, math and science were the subjects I really enjoyed. I was happy the days I had these subjects (laughter).

Zierler:

Juan, given your abilities, even as a child growing up, did you ever think about pursuing an undergraduate education farther away from home? Perhaps going to the United States or Europe for your college degree?

Maldacena:

No, that wasn't an option.

Zierler:

It wasn't an option? You wanted to stay close to home.

Maldacena:

I think it would have been unaffordable. It didn’t cross my mind. My parents had both gone to the University of Buenos Aires, which was viewed as the best option.

Zierler:

Now, is the Argentine higher education system, is it more like the United States, where you go in and you have a general education and then you declare a major alter on, or it's-

Maldacena:

No, no, no.

Zierler:

More like the British system?

Maldacena:

It is more in the European style. Argentina tries to copy European institutions more than U.S. institutions.

Zierler:

So, the idea is that you declare a focus from the beginning?

Maldacena:

Indeed, you declare a focus from the beginning. In addition, the university is split geographically. There is one building in Buenos Aires where you study, let's say, law, and there's a completely different building where you study engineering, and yet another one, far away, where you study physics, biology and mathematics, etc.

Zierler:

So, you were in that third building?

Maldacena:

Yes.

Zierler:

And did you declare the major in physics right away? Is that what you knew you wanted to pursue?

Maldacena:

When I was finishing high school, I was doubting between engineering or physics. The most natural option would have been to be an engineer, because I liked technology and I liked repairing things.

Zierler:

Now, is your father's background in engineering with the elevator company?

Maldacena:

Yes, my father is an engineer, and he liked fixing things up in the house and I used to help him.

Zierler:

What was his reaction when you wanted to pursue physics? Did he think perhaps that that was not as useful a career option?

Maldacena:

My parents certainly thought that it wasn't a useful career option, but they were very encouraging, and they realized I was interested in it. And they probably thought that I would do this for a while and then I would come to my senses and do engineering, or something more practical, but-

Zierler:

That did not happen (laughter).

Maldacena:

No, but they were always very supportive. They always insisted that it was important to pursue what one finds interesting.

Zierler:

Juan, what were some of your favorite classes in physics as an undergraduate?

Maldacena:

When I entered the university, I liked my math classes. I loved calculus, which I had not taken in high school. I also enjoyed going through the proofs of the various statements and appreciating its nice logical structure.

Zierler:

Did you ever think about pursuing a degree in math itself?

Maldacena:

Yes, I did. But eventually I decided not to. I was set to go to a Physics Institute in Bariloche, another city in Argentina. If it had been possible to study math in Bariloche, maybe I would have done it. In fact, when I went to the Physics Institute, I continued doing some math courses, on my own.

Zierler:

Now, the Physics Institute, that's separate from the University of Buenos Aires?

Maldacena:

Yes. It is an independent institution called the Instituto Balseiro in honor of its founder.

Zierler:

Juan, did you ever think about experimental physics? Or you knew theory, based on your interest in math, was always going to be your path?

Maldacena:

Yes, theory was the more natural option, given my interest in math. The Instituto Balseiro had a very good experimental training. We had to take many experimental courses, we were encouraged to design new experiments, to make variations on existing ones, etc. But I still preferred the theory part.

Zierler:

Juan, when was your first interaction with string theory? When did you first learn about it?

Maldacena:

At this institute, we did a research project during our last year, it was somewhat similar to a master’s thesis. At about that time, Gerardo Aldazabal, a young professor, returned from Trieste, Italy, where had done a postdoc in string theory. He became the first-string theorist at the institute. There was already a small particle theory group working in quantum field theory and particle phenomenology. A project in string theory seemed an interesting option because I would learn both quantum field theory and general relativity.

Zierler:

Now, would this have been the equivalent of a master’s degree in the United States?

Maldacena:

Yes. In Argentina, it is called “licenciatura.” The total time I studied was six years, counting also the time at the University of Buenos Aires

Zierler:

And you could have stayed there for a doctorate if you wanted?

Maldacena:

Yes. In fact, many of my classmates stayed there for a doctorate.

Zierler:

Juan, I'm very interested in the ups and downs of string theory. You know, going all the way back to really right when you were born in 1968, 1969.

Maldacena:

Yes.

Zierler:

You know, there are moments when things are very exciting, and there are moments when things seem not so exciting. Where was string theory when you first started to think about it on a sustained basis? What were the exciting possibilities at that time?

Maldacena:

At that moment it was very exciting. Or at least, that is how I perceived it. In '84, the anomaly cancellation mechanism was discovered, and this created great interest. Gerardo Aldazabal had gone to Trieste shortly after that. When we went there, Abdus Salam, who was the director, told him, "You can work on whatever you want, but if you want to talk to people, you’d better work on string theory" (laughter). So, he learned string theory.

Zierler:

So, it was, in addition to being interesting to you, it was a smart career option as well?

Maldacena:

In retrospect, you can say that.

Zierler:

Now, did you have a thesis at the institute?

Maldacena:

Yes.

Zierler:

What did you write on?

Maldacena:

It was about deriving Einstein’s equations from the condition that strings propagate consistently on a curved manifold. This had been done previously by D. Friedan. But the goal was to do it in situations preserving spacetime supersymmetry.

Zierler:

Juan, did you get advice from your mentors that it would be best to leave Argentina to pursue your degree elsewhere?

Maldacena:

Yes, Gerardo Aldazábal told me that he had been happy to direct my master’s thesis, but that he advised to go somewhere else for a doctorate. So, as I was finishing my studies, I applied to various graduate schools.

Zierler:

Were you considering Europe as well, or you were focused exclusively on degrees in the United States?

Maldacena:

I thought about Europe, and some of the people from the Institute had gone to Europe. The application process to the U.S. was more straightforward. In Europe, it was a little more complicated. You had to know someone, and I didn't know anyone-

Zierler:

What programs were most compelling to you in the United States?

Maldacena:

I actually looked quite broadly, from engineering to physics. In the end, I applied to physics graduate schools. I was admitted to Princeton and the University of Florida. Princeton was my first option, so I came here.

Zierler:

Did you specifically know you wanted to work with Curt Callan?

Maldacena:

I talked to various people, and I ended up working with Curt Callan.

Zierler:

And how did you develop that relationship with Curt?

Maldacena:

At Princeton, during the first year, you take courses, do an experimental project, pass some exams, etc. After that, for the first summer, I was looking for a summer job and I talked to Curt, and he gave me a problem for the summer, and that's how I started.

Zierler:

And what was his research? What was Curt working on at this time?

Maldacena:

He was working mostly on two-dimensional conformal field theories. This first project was on two-dimensional conformal field theories in hyperbolic space. I really did not make much progress, but I learned about hyperbolic space, which was useful for later. After that, he gave me a different problem, involving conformal field theories with a boundary. This time we made some progress, and we wrote the first paper.

Zierler:

Juan, how was your English before you came to the United States?

Maldacena:

That is a good question (laughter). My mother, being an English translator, tried to make sure that I learned English. But I am not very good with languages. Especially for oral communication, the proper pronunciation, etc. When I came here, my written and reading English was reasonable. But it was hard for me to follow what people were saying, and it was difficult for me to speak in real time.

Zierler:

Did you spend much time at the Institute? Was that an interesting place to go for seminars and things like that when you were in graduate school?

Maldacena:

I spent most of my time at the university, but I would come to the Institute for seminars. A few times I went to some meetings that Frank Wilczek organized for students at his house. During my last year, [Ed] Witten gave very useful lectures on dualities and the latest papers.

Zierler:

In what way were Witten's lectures useful? What do you mean?

Maldacena:

It was after the developments of dualities, both in quantum field theory and string theory. He started saying, that he would review some papers. But new papers kept appearing and he could quickly summarize them, extract the important ideas, and explain them in a really simple and understandable way.

Zierler:

Juan, what was your process for developing your thesis topic?

Maldacena:

With Curt, we worked on conformal field theories with boundaries for a while. At the time, the main motivation were applications to condensed matter physics. This involved impurity models such as the Kondo model. I wrote a few papers on these topics. One is even in the Condensed Matter Archive. But I felt that I wanted to do something more central to string theory, involving black holes.

Zierler:

And by "central," what were some of the big, unanswered questions, or most promising avenues of research in string theory at this time?

Maldacena:

At the time, people were very focused on string compactifications and Calabi–Yau geometries. It was a fairly well-developed subject involving a great deal of mathematics. But there were also some intriguing ideas about strings and black holes. I thought that was interesting. With Curt’s encouragement, I started to think about this subject. I also heard lectures by L. Susskind and Ashoke Sen who were comparing the entropy of strings to that of black holes. Around that time, A.W. Peet came as a new postdoc to Princeton, having worked on various black hole solutions in supergravity. We collaborated on a paper that involved finding oscillating string solutions in gravity with the goal of making a better connection to Sen’s ideas.

Zierler:

Juan, I'll test your memory. Who was on your thesis committee?

Maldacena:

Curt Callan, of course, Larus Thorlacius and Kirk McDonald, an experimentalist.

Zierler:

Given that there was an experimental person, I'm curious at this time. What was going on in the world of observation or experimentation that may have been relevant for your research?

Maldacena:

Well, relevant to my research at the time, nothing. The most exciting thing that had happened was the discovery of the cosmic microwave background anisotropies. Also, when I started graduate school there was excitement about the SSC (Superconducting Super Collider), but it was cancelled shortly after. I don't remember whether it was in '92 or '93.

Zierler:

'93.

Maldacena:

In fact, as part of the first-year requirements, you had to work on a research topic. I worked for a particle experimentalist, Milind Purohit, on Monte Carlo simulations for the SSC. Looking at the feasibility of parity violation experiments with B mesons.

Zierler:

Did you enjoy it? Was this a fun diversion from your other interests?

Maldacena:

Actually, I could not get it to work. In other words, my computer program was not very good at finding the B mesons in the simulated data. And the professor was losing his patience with me.

Zierler:

Better to stick with theory for you?

Maldacena:

Yes. But it was useful for me to appreciate what experimentalists do.

Zierler:

Juan, on the personal side, when you came to Princeton, did you come with the sense that you would be making a life for yourself in the United States, or did that decision come later on?

Maldacena:

When people asked me at the time whether I was planning to stay. I said I did not know, but that, statistically, I was going to stay. Most people who had come from Argentina in similar circumstances had stayed.

Zierler:

Did you think about professorships in Argentina? Did you give that any thought later on?

Maldacena:

No.

Zierler:

Tell me more about how your thesis research developed.

Maldacena:

During my last year, Joe Polchinski discovered D-branes. These are soliton-like objects in string theory that have a very precise mathematical description involving strings ending on spacetime surfaces. In other words, strings with boundaries. I was in a very fortunate position because, for my previous projects, I had worked on conformal field theories with boundaries, so I knew all the technical tools. I also had worked on black holes. So, I immediately started thinking about the connection between D-branes and black holes. Then the paper of Strominger and Vafa came out, which was the first precise match between the entropy of extremal charged black holes and a counting of microstates based on D-branes. Then I wrote another paper with Curt where we attempted to extend this agreement to near extremal black holes, black holes with a non-zero Hawking temperature. It was a close but not a perfect agreement.

Zierler:

And what's the significance of the fact that the agreement was not perfect? What did that tell you?

Maldacena:

It told us that we were not doing it the right way. In later papers, we found other cases where the agreement was more precise. It was a bit experimental in the sense that you computed these entropies from the D-brane side and then from the gravity side. But it was an uncontrolled approximation, the D-brane calculations were done at weak coupling but the gravity ones at strong coupling. In fact, in some cases they matched and some other cases they didn't match.

Zierler:

Juan, what would you say looking back was the significance of this work in terms of what came afterwards?

Maldacena:

It was very significant for me, because it convinced me that there was something interesting about this connection, but that it had to be understood better. Writing that paper with Curt also opened many doors for me in terms of contacting other researchers. I was invited to give talks at Santa Barbara, Caltech and Stanford. It also led to a very fruitful collaboration with Andy Strominger.

Zierler:

And then for your postdocs, what were you considering?

Maldacena:

I had already accepted a postdoc offer from Rutgers University. That process had happened before the D-brane and black hole development.

Zierler:

And who were you working with at Rutgers?

Maldacena:

There was a wonderful group at Rutgers, with Tom Banks, Michael Douglas, Dan Friedan, Nati Seiberg and Steve Shenker. I did not work with them, nor with the other postdocs that were there at the time: Eva Silverstein, Ofer Aharony, etc. But I had wonderful discussions with them.

Zierler:

Juan, did you see your research at Rutgers as a continuation of what you were doing in graduate school, or were the-

Maldacena:

Indeed, I continued to write papers on black holes and D-branes, some by myself and some with Andy Strominger. At the time, most of the Rutgers group was working on the matrix theory proposed by Banks, Fischler, Shenker, and Susskind. It is a very interesting way of thinking about 11-dimensional M theory. It was another interesting application of D-branes. Being able to follow closely this work in matrix theory also helped me for what came later.

Zierler:

Juan, more generally at this time, more and more theoretical physicists are finding the utility of computers. I'm wondering at what point this became useful for your research?

Maldacena:

I never really used computers in a serious way. Of course, I sometimes used symbolic manipulation programs (such as “Mathematica”). But some of my collaborators are very good with computers and have used them in an important way in joint projects.

Zierler:

How did the opportunity at Harvard become available to you?

Maldacena:

Andy Strominger had just moved to Harvard. And he convinced the department to hire me. First, I was hired as a visiting professor for one year. During that year, I wrote the paper on AdS/CFT.

Zierler:

Juan, did you know immediately how significant AdS/CFT would be?

Maldacena:

I thought it was a very interesting paper, but I did not envision at the time all the applications that people would later find. I thought that it was most probably true.

Zierler:

When you say, "probably true," what was the question?

Maldacena:

This paper consisted on a conjecture. Let me explain it. It was a continuation of the work on black holes and D-branes. There were hints of a connection between the two but its precise nature was unclear. In fact, there were two descriptions for these D-branes. One was the one found by Polchinski in terms of open strings, which was simpler at weak coupling. The other was in terms of black brane solutions, found by [Gary] Horowitz and Strominger, which was simpler when the coupling was strong. The key idea was to take a low energy limit where both sides simplify. The D-brane description becomes a theory similar to quantum chromodynamics, but with many supersymmetries. In the gravity description, one focuses on the region near the horizon of these black branes. This region has the geometry of anti-de-Sitter space. One piece of evidence for this equality was that the symmetries of the two sides match. That both sides had a scaling symmetry and a full conformal symmetry.

Zierler:

Juan, what was the significance of AdS/CFT on the holographic principle?

Maldacena:

When I wrote the paper, I wasn't thinking about the holographic principle. I knew about it, but it was not high in my mind. The connection to the holographic principle was made later by Witten. At the time, I was more inspired by the relation between QCD and string theory. In fact, the idea that strong interactions involve strings was motivated by experiments and preceded QCD. Later it was argued by ‘t Hooft, that in the limit of a large number of colors one should expect to see weakly interacting strings. Then Polyakov advocated the idea that these QCD string should live in a five-dimensional space. And this fifth dimension ended up as the fifth dimension of the anti-de-Sitter space. But of course, AdS/CFT is a very precise realization of the holographic principle, describing a region of spacetime in terms of a theory at the boundary. It was precise, because it said what the theory at the boundary was.

Zierler:

Were you working with Ed at this time directly?

Maldacena:

No. But after my paper, he started to work on it and wrote an important paper where he made the relationship more concrete by providing a way to do many computations. A similar paper was written by Gubser, Klebanov and Polyakov. Actually, Gubser and Klebanov were also working on the connection between black holes and D-branes and their previous work was also very influential for me.

Zierler:

What was the impact of this research on our understanding of black holes?

Maldacena:

If you accept the conjecture, then any object living in the gravitating spacetime should be described by the field theory side. It says that black holes are described a thermal fluid in the field theory. This then gives a precise description of the microstates as well as their unitary evolution. In principle, it allows you to answer any question that you can pose about the black hole as seen from the outside. Nevertheless, the description of the black hole interior is still being worked out. The applications of the conjecture to other areas, such as condensed matter, were found later by other researchers and I was very surprised when they were proposed.

Zierler:

So, you stuck with your side interests in condensed matter? This was something you returned to?

Maldacena:

No, I have not really returned. Interestingly, the Sachdev-Ye-Kitaev model is actually historically related to the impurity models involving conformal field theories with boundaries. Except that in some sense one keeps only the boundary degrees of freedom! And it turned out to be a very nice model for some aspects of holography.

Zierler:

Juan, when would you say you started thinking about how string theory might be useful to cosmology? When did that happen?

Maldacena:

Are you asking about the non-gaussianities paper?

Zierler:

That's right.

Maldacena:

We had been doing many computations in anti-de-Sitter space and I wanted to see whether there were any lessons for de-Sitter. Edward Witten pointed out to me that the computation of non-gaussianities was an open problem. We discussed it for a while, but in the end, he dropped out from the paper and I continued to finish the calculation.

Zierler:

Juan, you were a full professor at Harvard for such a short amount of time. What were the circumstances of coming over to the Institute after only a few years at Harvard as a full professor?

Maldacena:

Well, the Institute made me an offer. I had a hard time deciding, I think both were excellent options.

Zierler:

Although it's in some ways a very different life. A different academic path, being in a-

Maldacena:

Yes, yes.

Zierler:

-physics department with students than being at the Institute.

Maldacena:

At the Institute we do work with graduate students from Princeton University. I had the good fortune to have had excellent students. Here you do not have to teach; you can focus on research. On the other hand, some people say teaching is good for you, so maybe I am missing something.

Zierler:

Now, do you have the option? Could you teach at Princeton if you wanted to?

Maldacena:

Yes, I have the option.

Zierler:

Have you ever taken advantage of that?

Maldacena:

No, I keep thinking that maybe I'll do it next year.

Zierler:

Juan, in terms of the collaboration opportunities, what was interesting or compelling to you to come to the Institute in 2001?

Maldacena:

Of course, the Institute had outstanding faculty members and also the Princeton Physics department was excellent.

Zierler:

Did you take on new projects or research that you might not have had you stayed at Harvard?

Maldacena:

That is very difficult to say.

Zierler:

Well, what did you start working on when you got to the Institute?

Maldacena:

I have continued working on aspects of AdS/CFT, problems in quantum field theory and string theory.

Zierler:

When did you start working with Lenny Susskind?

Maldacena:

A very interesting paper by Almheiri, Marolf, Polchinski, and Sully (AMPS), presented an important paradox regarding the black hole interior. I had a model for how to circumvent it, which turned out to be wrong. But I discussed it with Lenny. We discussed the full Schwarzschild solution and its interpretation as an entangled state, on which I had written a paper some time before, based also on previous work by W. Israel. One could state this as ER=EPR, in reference to the papers on the pair of black holes of Einstein and Rosen and the one on entanglement by Einstein, Podoslky Rosen. It turned out that this had interesting lessons for the paradox that I just mentioned.

Zierler:

Juan, chronologically, we've worked sort of up to the present day, so I'd like to ask a few general questions, science questions, about the development of the current state of research in a few areas. One is, when did you start to really think about the connections between space-time and entanglement? When did that start, and what's the state of the research today?

Maldacena:

The first time, for me, was the paper I wrote in 2001 on the eternal black holes. It stated the relation between this solution and entanglement. Actually, W. Israel had said something similar many years before. But I did not realize its full implications at the time. Later, Ryu and Takayanagi conjectured a formula for the entropy of a region in terms a certain minimal area. At the time, I thought that the Ryu–Takayanagi conjecture was too simple. That it was probably wrong. However, many other papers presented more evidence. And of course, what made it interesting was precisely that it was very simple! Eventually, we wrote a paper with Aitor Lewkowycz connecting the Ryu-Takayanagi formula to the gravitational path integral. In other words, generalizing the Gibbons Hawking argument for black hole entropy to the von Neuman entropy in more general cases. The most interesting development in this direction was the recent computation of the entropy of Hawking radiation, in work by Penington and Almheiri, Engelhardt, Marolf and Maxfield. But I think that there are still further connections to be found between entanglement and geometry.

Zierler:

Juan, the word "chaos" means very different things depending on your research focus. What does this word mean as it relates to things that you're working on?

Maldacena:

Of course, the fact that black holes are black, or very good absorbers, suggests that they are rapidly thermalizing systems. And for that, you need some chaos. Hayden & Preskill and Susskind & Sekino argued that black holes scramble information very efficiently. An important property of black holes is that time evolution acts as a boost (a Lorentz transformation) in the near horizon region. This implies that two particles that enter or come out from the near horizon region at different times would have a very large relative velocity. ‘t Hooft showed that this implies that their gravitational interactions become larger the larger the time difference between the two. This, in turn, makes it harder to make predictions. This was interpreted as a manifestation of chaos or the “butterfly effect” in papers by [Douglas] Stanford and Shenker and [Alexei] Kitaev.

Zierler:

Juan, a very broad question that's going to touch on many aspects of your career, where do you see your work fitting in the overall effort to resolve conflicts between general theories of relativity and the quantum field theory approach?

Maldacena:

The general goal of theories of quantum gravity, such as string theory, is to make quantum mechanics consistent with a dynamical spacetime (general relativity). And this is has been the general area of my research.

Zierler:

But the question is, I mean there's many different approaches to try to resolve the conflict. What do you see your research- what's the unique approach of your research that has promise to resolve these conflicts?

Maldacena:

I have been following the general approach of string theory. String theory is a theory under construction, we know some aspects of it. The AdS/CFT duality is giving us some way to study some quantum spacetimes. But many important conceptual questions still remain.

Zierler:

Do you see your research having specific import on the search for dark energy or dark matter?

Maldacena:

No. I do not see any connection at present, unfortunately.

Zierler:

It would be great if you did.

Maldacena:

One could say that in anti-de-Sitter the sign of the dark energy is wrong, as compared to our own universe. So, we made a sign error (laughter).

Zierler:

How do you mean?

Maldacena:

Our universe is more similar to de-Sitter than anti-de-Sitter. We studied anti-de-Sitter because it is simpler, but the ultimate goal has always been to understand de-Sitter space or cosmological spacetimes in order to understand the beginning of the Big Bang. We hope that anti-de-Sitter will be a steppingstone towards that goal.

Zierler:

Juan, another very broad question and that is, you know, string theory evokes very strong reactions from physicists. Either people who are strong proponents of it to people who are not. And as I'm sure we can both think of particular names, that's not necessary, but if we were to create a caricature of somebody who would say, "I'm no longer patient with string theory. It's been around for too long. It hasn't shown us all of the promises that were there." So, I guess maybe there are three ways that I might ask you to answer that sort of approach. The first would be, what would be a repudiation of that assumption in terms of, actually, no, this is something specific or concrete that string theory has really shown us in the here and now. Another approach to the impatience might be, we're really on the cusp of something exciting and we're going to continue working on it. because we see a path. And to what extent might you concede, actually, some of the things that we thought might be achievable, there real no path forward that we can see at this point?

Maldacena:

The minimal thing you can say about string theory is that it gives us a model for quantum gravity, for the quantum mechanics of spacetime itself. We do not know yet whether it is the theory that describes Nature. Physics is an experimental science and we will not know whether it is the right theory until we can successfully compare it to experiment. The ultimate goal of quantum gravity is to understand the very beginning of the Big Bang. We are not there yet. In fact, the theory is not understood well enough to really address this question. Nevertheless, string theory has a rich mathematical structure that has shed light into aspects of quantum field theories, mathematics, etc.

It is important to distinguish two things: one is string theory as a theory, the other is the sociological community of so called “string theorists.” These do not always work on string theory per se. They can work on quantum field theory, aspects of condensed matter, mathematics or more conventional cosmology. I was once asked to give a “vision” talk at one of string theory conferences. I proposed that we should think of STRINGS as an acronym for Solid Theoretical Research into Natural Geometric Structures. I would define it as working on fundamental theories. Fundamental in the sense of exploring the more basic principles, those of of quantum mechanics, relativity and spacetime. These basic principles were discovered in the beginning of the 20th century and have not yet been modified. We would like to understand how to put them together theoretically. Steve Weinberg once said that our main problem is not that we take our theories too seriously but that we do not take them seriously enough. In this spirit, the idea is to take seriously these fundamental principles of twentieth century physics and to understand better their implications. Science mainly goes forwards thanks to experimental observations. However, it can also move forwards by understanding the logical consequences of previous ideas. On the question on whether one should be impatient or not, one would have to judge the intermediate results. I think that they are interesting, and they keep motivating us to continue in this direction.

Zierler:

Yeah.

Maldacena:

And I think if you take general relativity and quantum mechanics seriously, you have to put them together in some way. “String theorists”, are happy to consider other possibilities. For example, the SYK model. It is certainly a very interesting model that displays a form of holography, but there is no obvious string. However, it is part of what string theorists work on. Simply because it is a model that sheds some light on aspects of spacetime and quantum mechanics. So, it fits into the definition of “STRINGS” as an acronym. Another aspect is the connection between quantum information and gravity. A lot of the work in that area is independent of the traditional ten-dimensional superstring theory, relying instead on gravity as an effective field theory. Or course, it was motivated and guided by examples coming from string theory and AdS/CFT.

When string theory was discussed as a theory of nature in the mid 80’s the main guiding idea was Grand Unification, the idea of a very big symmetry that comes from string theory. Then there would be a simple six-dimensional internal geometry and we would derive the properties of elementary particles. It is still a very compelling idea, but the details seem more difficult than expected. There are many internal spaces and it seems difficult to analyze them all. The current approach is now to make statistical prediction or to find out which type of physics is definitely impossible to obtain from such spaces. But, let me be more provocative and say that strings have already been experimentally discovered.

Zierler:

Good!

Maldacena:

In fact, they were discovered even before string theory was invented. And these are the strings of strong interactions. They are formed when you separate a quark and an antiquark. They are real relativistic strings, they stretch, their tension has been measured, etc. Now, people would say, "Oh, no, this is a very different kind of string. It's not the string that describes gravity. It's the string of Quantum Chromo-Dynamics". But we now understand that there is a close connection between the QCD strings and the strings of gravity. In theories that are similar to QCD, like its maximally supersymmetric version, this string becomes the string of quantum gravity. Of ten-dimensional string theory. This shows why string theory is a reasonable idea, and that it is not very far removed from the physics we already know. If you really care about gauge theories and the strong interactions, it is useful to consider the string perspective. In fact, already from the ten-dimensional strings there are some interesting lessons. For example, there was a conjectured lower bound on viscosity, which arose from a black hole perspective, found by D. Son and collaborators. There has also been some interesting lessons for scattering amplitudes.

Zierler:

Juan, would you point to QCD for the general criticism that string theory is not testable?

Maldacena:

I have pointed to it for the basic idea of relativistic strings, as objects existing in nature. The precise mathematical description for the string theory that describes QCD is not yet known. Even once we know it, critics can still say, "Oh, this is just the QCD string, not the string of quantum gravity." And they would be right, to really test string theory as a theory of the dynamics of our own four-dimensional spacetime we would need something else.

Zierler:

Juan, a truly abstract question, and I know there's no way to even experimentally think about the possibility, but if you had to bet one way or another, do you think there's multiverses?

Maldacena:

I think that the multiverse explanation is the simplest explanation of the cosmological constant in a theory where it is not a fundamental parameter.

Zierler:

Why?

Maldacena:

Suppose we have a theory where the cosmological constant is in principle calculable, as in string theory, where it depends on the details of the internal geometry. Then its natural value is very large in magnitude, but it could have either sign. As we vary the details of the internal space it would vary in an apparently random way. So, if you have a huge number of solutions, it is possible that one of them has the observed small value. So, you can accommodate the observed value. It is possible that in other regions the universe has a different internal shape, and that all possible solutions exist somewhere. A good question is how we should think about this multiverse. Whether they all exist at the same time in distant regions, or that they just all exist as mere possibilities, as in the many worlds of Everett. It is also possible that this multiverse might be important for getting rid of the initial singularity.

Zierler:

You mean the initial singularity of the Big Bang?

Maldacena:

Yes.

Zierler:

Juan, as you mentioned, the sociology of strings, of course another area in which people in the field or beyond the field have very strong opinions about string theory is about the number of people who devote their research to it. And of course, at Harvard there were many strong feelings about this as well. Partly when you were there. And so, I guess my question is, you know, over the years, people have said there haven't been enough people in string theory, there have been too many people in string theory. What is your general response to that, and where is the field now in terms of the "right number" of people working on these questions?

Maldacena:

I think that the problem of understanding the quantum mechanics of spacetime is important, and that progress is being made. It is always difficult to say, what the size one field should be relative to another. It is not a decision that should be made very abstractly. One should look at the strengths of the candidates in various fields. Of course, there are several fields in physics that are expanding rapidly, like quantum computing, certain aspects of condensed matter or gravity waves. As a general science policy, it is important to have a diverse and balanced research portfolio. There should be research ranging from the very practical to the very abstract. The important ideas in physics often arise in one subfield and then they percolate to others where they are applied in novel ways. The different sub-fields exit just because of our limitations, and the general tendency is towards unification, towards general ideas that can be applied more widely. An example of such an idea is scaling symmetry and conformal symmetry. It can be applied to condensed matter, to high energy theory, to cosmology, to quantum gravity, etc. It is always the same idea, sometimes with little tweaks that are special to each sub-field. In physics these very general connections are very valuable.

There are also big motivating questions. Among them is what is the nature of spacetime. String theory tackles this big question. It is a question that, right now, can only be tackled theoretically. Nobody has come up with a good experimental way to answer it. Probably, the most promising experimental avenue is to look for gravity waves from inflation, at least within the next few years.

Zierler:

Juan, are there any awards or recognitions you've received that are most personally meaningful to you?

Maldacena:

I like to think that what really matters is writing good papers and not the awards. For me, the most significant opportunity was to have been offered the professorship at the Institute.

Zierler:

So, I'll substitute the question, then. Since you emphasize the importance of the papers, is there any particular paper that you're most proud of?

Maldacena:

I would go for the AdS/CFT paper.

Zierler:

And to the extent that you have a sense of the next generation in string theory, and your interactions with graduate students or postdocs, or you know, interacting with people at the strings conference and things like that, where do you see the field headed in terms of the next generation coming up and the things that they're working on?

Maldacena:

The next generation is exceptionally strong. There is a wonderful group of young people who are working in a variety of topics. One, is the connection between quantum information and gravity. People like Douglas Stanford, Geoff Penington, Ahmed Almeiri, Daniel Harlow, Aron Wall, and several others have been obtaining excellent results. Another interesting topic has been centered on bootstrap ideas, the idea of solving theories by applying consistency conditions. This is an idea with a long history, and one fairly central to string theory ideas, but which was recently invigorated by new numerical and analytical ideas. Others are using ideas of topology and sophisticated mathematics to classify quantum field theories and phases of condensed matter systems. There are also exciting new discoveries in the structure of scattering amplitudes in field theory and gravity.

Zierler:

Of course. The idea is there's lots of interesting things to work on for the next generation.

Maldacena:

Yes, more than I can follow (laughter).

Zierler:

So that leads me, Juan, to my last question which is, as you look forward in your own career, what are the things that you want to work on, both that inspire the most curiosity in you, and the things that you feel are the most fundamental, unanswered questions that, you know, to go back to the beginning of our conversation, when we come out of the pandemic, and you're not working on these sort of sidetrack projects, when we get back to normal and you feel like you're back on the kinds of big questions you've been on over the course of your career. What are those big questions that you feel are most fundamental and also the most fun for you to work on as you look forward?

Maldacena:

I would like to understand better the black hole interior. We have a reasonable understanding of the black hole as seen from the outside. The importance of interior is that it has the singularity similar to the Big Bang singularity. Well, it is really a big crunch singularity, the opposite of the Big Bang. We hope that understanding the black hole singularity will help us understand the Big Bang singularity in the early universe. This is the long-term goal. But there are many questions related to the black hole interior that need to be understood better.

Zierler:

What will it take for us to get there? In other words, what do we know about the black hole exterior that might be useful for getting us to better understand the black hole interior?

Maldacena:

Recently, a very useful tool has been the fine-grained entropy formula, or the Ryu–Takayanagi formula. Solvable toy models, such as SYK or special two-dimensional gravity theories also play an important role.

Zierler:

Of course. Well Juan, I want to thank you so much for spending this time with me. I really appreciate it.

Maldacena:

Sure. Thank you too.