ICTS

SM: You are saying it was too intimidating.

SW: Yes intimidating and one just kept quiet. There was also a hostile atmosphere. So I didn’t say anything about what I was doing … the third order phase transition.

SM: But had you already solved the equation?

SW: Of course.

SM: You had the two solutions; you knew there was a phase transition?

SW: Absolutely. I solved it by a dumb person’s method. Using the method [I mentioned] anybody can do it. If you look at the paper of Gross and Witten, you have to guess the analytic function just like in the Hermitian matrix model that was solved in the famous paper by Brezin, Itzykson, Parisi and Zuber. My method was… to start with the equation and solve it straightforwardly. You can solve any such problem, with any number of branch cuts by mapping to the Riemann-Hilbert problem. [I had used the Coulomb gas analogy to intuitively understand the appearance of a gap in the charge distribution, which would be described by 2 different functions. This I knew from the book `Statistical Theories of Spectra: Fluctuations’ edited by C. E. Porter, which was emphasized to me by my friend Vivek Monteiro].

I was talking to Leo Kadanoff about this subject all the time. He felt that … the order parameters... looked like the order parameters of Sherrington and Kirkpatrick for spin glass. So then I told Leo what had happened during the visit of David Gross. You know what he did? He picked up the phone and called David Gross in Aspen. I was there in his office. He said, ‘I have a young man here who has done this, this, this...’ There was a long conversation actually. He then put down the phone and said, ‘now he cannot f*** you over.’ Exactly those words! [Kadanoff knew that I had solved the problem.] But there was a lot of pressure in the high-energy group to mention Gross and Witten’s work in the paper I wrote [denying me the credit]. Only a couple of years ago I just rewrote it and sent it out on the arXiv the way it had to be!

Immediately after this work on the 3^rd order transition I invented a 0+1 dim gauge theory and solved it exactly. At large N it exhibits the same transition I had found in the unitary matrix  integral, and published it. The large N transition occurs in this model when the Fermi level of the associated fermion theory reaches the maximum of the potential.

SM: Sumit was also there in Chicago then. You worked with him.

SW: Yes, Sumit Das was a student then.

We wrote two papers together. One was on electric-magnetic duality. The other one was the reduced Eguchi-Kawai type model. It was a good proposal but what they [Eguchi-Kawai] did was not justified. But at times, other people can develop good ideas further. Giorgio Parisi wrote a beautiful paper on how to understand the Eguchi-Kawai suggestion in terms of quenched random momentum phases. Sumit and I wrote a paper applying this idea to Yang-Mills theory and understood the randomization of the translation group, which is sitting as a subgroup in U-infinity. There was a competing paper from Gross and Kitazawa. David Gross and I have had lots of interactions...

AD: The work on confinement that you did with him [Sumit], you wrote it up 20 years later in India.

RG: There is one with Sumit where you had pointed out an error [in Polyakov’s work]. That was published in 1982.

SW: Yes, yes that was the electric-magnetic duality paper. If you want me to summarize that briefly – Polyakov made a truly profound contribution in showing that in the confinement phase of a gauge theory in 2+1 dim. can be understood in terms of a plasma of monopoles [coulomb gas] that gives rise a massive particle in the spectrum and confines integer charged quarks. The would be long-ranged correlations become short ranged. That was Polyakov’s great physical insight. That paper is part of a trilogy by Polyakov in 1976.

RG: Instantons, monopole plasma... ?

SW: The instanton paper [in 4-dim Yang-Mills theory], then the 2+1 dim. Abelian [lattice] gauge theory paper and there is one more on the renormalization of sigma models and geometry. These papers were special – physics before and after them is different.

Then what he did is to apply this idea of confinement to SU(2) gauge theories. That too became one of Polyakov’s famous papers. I will tell you what his mistake was. He made a singular gauge transformation on t’Hooft-Polyakov monopole solution that has unit monopole charge in units of the basic electric charge. This is a gauge transformation to a unitary gauge. He then ignored half the flux that is there on the Dirac string in this singular gauge. That reduced the monopole flux by half. So now you’ve got a Dirac monopole. His plasma of monopoles had half integer charged monopoles and they obviously confine integer charged quarks because the half integer monopole plasma will screen the integer charged quarks. So this was what he had in the paper and it was wrong. First SU(2) gauge theory does not have integer charged quarks in the fundamental representation. We basically found that there was a mismatch between the magnetic gauge group and the electric gauge group that brought out the importance of the centre of the gauge group, a fact that was already emphasized by ‘t Hooft. We wrote a paper on this and I gave a seminar at the Enrico Fermi Institute. Leo [Kadanoff] was there at the seminar and he came up and told me, ‘you must have got up fresh in the morning to find a mistake in Polyakov’s paper.’ Then I wrote a letter to Polyakov. I think I have that reply somewhere. He got really upset. He wrote, ‘I cannot make a mistake like that. It’s just a matter of normalization.’ It cannot be normalization! He didn’t admit it. So anyway, that’s how it was.

 

Return to India…

I came to India thinking about the [mentioned above] reduced [Eguchi-Kawai] models. On the way I had stopped in Les Houches for the summer school and Kitazawa and I worked on the Hamiltonian reduced model. If you look at gauge theories in 2+1 dimensions, then those theories can be basically written in terms of a single unitary matrix...in a certain gauge. So I said, ‘fantastic! Single matrix Hamiltonian and one should be able to solve this model.’ No chance...because there are no symmetries due to the quenched random phases. So you cannot solve this problem. This was the problem with which I came back to India. I kept on working on this for one year.

 

Quark Confinement and QCD…

RG: When you came back to India with this kind of background, what was your state of mind about physics? Did you feel there were lots of problems you wanted to tackle? Did you feel you would have a program?

SW: Yes I came with a program.

Before that let me tell you another related story. One day Nambu and I went out to dinner with Steve Adler and on the way back he [Nambu] was dropping me at my house. He stopped the car, put his hand on my knee and said, ‘look, the problem you are trying to solve is too hard. You should be a little careful.’ See, my problem was that I wasn’t writing any papers because I wanted to solve the quark confinement problem. I had this in my mind that oh if I could just solve this it would be fantastic. Maybe Nambu is old so he cannot solve it. I tried and tried but I failed. So I came back with that program – to work on quark confinement and QCD. Then something very interesting happened. I was invited to give a lecture course in the Cracow school in Poland. My old friend Mike Peskin was also there. He is the guy who told me all about the paper by Witten on current algebra...the Wess-Zumino-Witten term. Michael Peskin is an amazing expositor.

I was thinking: all this math stuff? How would Nambu think about this? After all a meson is made of two quarks so there must be a fermion model underlying this. I still remember I was at the airport at Krakow and I wrote this [model] down...I knew that quantum chromo-dynamics has a mass gap. So if I integrate all the gluons mentally what would I be left with? I would be left with an expansion in terms of fermion operators. And the coefficients would be related to the mass of the glue-ball. What emerges is a non-linear fermion model. At that moment I didn’t realize that this was a Nambu-Jona-Lasinio like model if one retains only the lowest dim operator. Very shortly I did! Heisenberg originally invented this model, and this is mentioned in the Nambu-Jona-Lasinio paper.

I think by the time I came back, Avinash and I were sort of talking a little bit.

AD: I remember how excited you were about this.

SW: Yes, I felt finally we were making some progress in QCD.

SM: The work of Witten you talk about is the non-Abelian bosonization?

SW: No. The Wess-Zumino-Witten model.

RG: The 4-dimensional current algebra. The 5-dimensional Wess-Zumino-Witten term actually which he later specialized to 3-dims.

SW: That was later.

SM: Oh the thing that gives you the anomaly in the Chiral-Lagrangian?

RG: Yes. Then Witten interpreted the baryons as solitons.

AD: The solitons were there. But how the solitons could be identified as baryons [for odd N] wasn’t clear. This paper made it very clear.

SW: Fascinating. So we wanted to understand this paper from a microscopic point of view. Then Avinash and I started collaborating. We knew the standard tricks of how to do the large N limit for the non-linear fermion models. At large N we can use factorization and Lorentz invariance to essentially work with the lowest dimension term in the non-linear fermion model. You have the chiral field, and then you integrate out the fermions. And then there is this determinant that you have to calculate...that is related to the anomaly a la Fujikawa. We solved this in some way – it wasn’t very satisfactory. But I think what we really found – and that was the most important point – was the differential equation in the space of the slowly varying chiral field for the determinant. And that differential equation we integrated in the space of chiral fields to find the 5-dimensional Wess-Zumino-Witten term. And we were very excited and delighted about that. I think that was the first important work that we did. At least the first important work I did in the Tata Institute. Shanks (Shankar) was a student then and we roped him in.

The problem was the determinant. There was a very important paper by Alvarez-Gaume and Witten on gravitational anomalies. If you read that paper very carefully – one of the most important technical things that they did was to give a definition of the phase of the determinant. There is a modulus and a phase. And we took this over and worked out everything rigorously and got the same answer as before.

AD: There was a rigorous perturbative calculation to see whether the five-boson vertex is there. That we could clearly see from the Nambu-Jona-Lasinio model. The only issue was how to write the non-perturbative determinant. Usually if there is a gauge field, you know how to do it. But there is no gauge field here as it is just a four-fermion model. So we had to do a lot of hand waving and inventing background vector bosons – work out the terms and then set the bosons to zero. You still have the meson term that is left. Something like that was done. And number of colors popped out naturally because this was a model for quarks.

RG: So if I understand right the usual formulation you write in terms of the unitary matrix. But now this is effectively writing the unitary matrix as an exponential of the pi-meson field.

AD: Yes yes.

SW: I felt this was very nice, because we could do something about QCD at long wavelengths in the large N limit in this particular [chiral] sector. This project became Shankar’s PhD thesis.

There was a competing paper on evaluating the determinant by Polyakov-Wiegmann. In those days there was no Internet. They also did the determinant calculation. The good thing was that it felt like playing basketball with Michael Jordan. We also played on the same court! Polyakov was there.

SM: It sounds from your description that you were motivated mainly by the aim of understanding quark confinement and other aspects. Looking back now, the problem in some sense is not yet been solved. Do you feel that it’s an important problem and was the right one to tackle? What is your view on the problem?

SW: I think if one can make some headway one would have understood gauge theories differently. I still feel that we don’t understand gauge theories of quark confinement except by analogy or numerically on the lattice. There was this talk by Nambu at a meeting, I still remember. He said, ‘take a monopole and drop it into a superconductor’ if you have a monopole and anti-monopole there will be a flux string in between that explains the linear potential. We understand that in terms of our understanding of superconductivity. After that Mandelstam and t’Hooft conjectured that the QCD vacuum behaves like a magnetic superconductor and that explains the confinement of `electrically charged’ quarks. I think the achievement of Seiberg and Witten many decades later was to realize this idea in a weakly broken N=2 supersymmetric gauge theory. But without supersymmetry, it’s like working on the real line rather than the complex plane. Then it is very difficult – we don’t understand these things, but Seiberg-Witten solution may have a hidden message. Certainly it would be fantastic if somebody can solve this problem. [You will get rich as well... there is a million dollar prize for showing that a mass gap exists in a non-Abelian gauge theory in 3+1 dims.]

SM: But you know there are some problems you solve and get very famous for, but they don’t lead to much progress. And there are some problems that are very rich and go very far. Which do you think this quark confinement problem is like?

SW: Because it is so complicated, the quark confinement problem led us to so many other things. It led us to exploring matrix models, supersymmetric theories, lattice gauge theories etc.

SM: So the attempt proved very fertile.

SW: Yes. It’s like the Riemann hypothesis. As you know it’s one of those great math problems, but in order to solve that problem, an amazing amount of new math has come out.

RG: I think in the quark confinement case also, it would depend a bit on how it is solved. If it is a purely mathematical demonstration, in epsilons and deltas, then it’s not probably likely to… As you said the Seiberg-Witten solution is an example of a whole rich field.

SM: Another analogy might be the question you brought up earlier on about renormalizability. The BPHZ [Bogoliubov-Parasiuk-Hepp-Zimmermann] stuff was great, but what did you learn from it? However the Polchinski-Wilson approach to renormalizability in field theory also did it, but it taught you so much.

SW: Yes, about the deep structure of quantum field theory.   

RG: So you mentioned travelling... and also that the general atmosphere in TIFR was not to travel.

SW: Yes that is true, but after the initial Nambu-Jona-Lasinio model work Virendra Singh did give me leave and I went to KEK. During that time we [Avinash, Shankar and I] were corresponding a lot. In the old days we used to do calculations and send them by mail. KEK had some brilliant people Hirotaka Sugawara who was the head of the theory group then and Makoto Kobayashi. I spent three months in that laboratory. I wondered what were the Japanese doing in experimental high-energy physics in comparison with what was happening in the West? Of course in hindsight, they were preparing for their big projects in high-energy physics!

There I was alone and I loved to hang out in libraries. I didn’t like sitting in offices. So I was just going around and wondering what else new I could do. In earlier times at Chicago I had worked on matrix models, and the first avatars of random surfaces in connection with Polyakov’s work on quantum geometry of strings. Friedan and Shenker were there in Chicago at that time. I was very familiar with the basics of string theory. So at KEK, I wondered that if in the work on the Nambu-Jona-Lasinio model, we go from four to two dimensions, we will have a string moving in this space of the chiral field, which is not a flat space. I thought of this idea – it was early 1984. As I mentioned after my mini-sabbatical at KEK, I went to Chicago. I mentioned this idea, of a new type of string theory, to Nambu and he liked it and found it interesting. I returned back to India after visiting SLAC and IAS Princeton.

In the summer of 1984 in Aspen, Mike Green and John Schwartz demonstrated anomaly cancellation in certain supersymmetric models of string theory. After that began the explosive interest in string theory because anomaly cancellation meant that there was a chance that string theory can describe chiral gauge theories of the real world. But I didn’t know any of this as we were far away in India. We didn’t get any mails, no seminars by visitors, nothing! The news came that this had happened and people were very excited. I remember that [during my visit to the US after KEK] I gave a seminar at the Institute of Advanced Studies on the Nambu-Jona-Lasinio model etc. I went to an office Witten was using but he was not there. His desk had only one paper and it was the review article by Schwartz. I noted that in my head, just noted it. I didn’t know what it all meant.   

RG: So this was before Green-Schwarz. Early 1984.

SW: Yes this was before the summer. Alvarez-Gaume and Witten had also written a paper on gravitational anomalies. So I suppose this [anomaly cancellation in string theory] was all building up in some sense?

I came from another direction, trying to do something new. I had no idea what had happened in the west. So I came back and started working on it with my two students – Sanjay Jain and R. Shankar (Shanks).

 

Nuclear Disarmament Movement…

Now something happened which I think was perhaps a strategic error of my physics life. There was a nascent nuclear disarmament movement in Bombay and given my left political leanings I encouraged my friends to join the nuclear disarmament movement. The People’s Science Movement was also going on, and so was the anti-nuclear movement. I felt that we should be doing something about that. Together with other activists Vivek Monteiro, Praful Bidwai, Achin Vinayak and Biswarup Banerjee (from TIFR), we had formed a Group in India for Nuclear Disarmament abbreviated as GROUND. We were all part of that. I was the scientist and convener. We spent an enormous amount of time in the anti-nuclear movement. This had started before I went to KEK Japan. When I was in Japan I actually went and met the Hibakusha. They are the survivors of the atomic bombing of Hiroshima and Nagasaki. I went to Hiroshima and met lots of people. I met Mr Iwakura and Ronny Alexander of the Hiroshima-Nagasaki Publishing Company. They were the people who created the ‘10-feet movement’. People contributed to buy 10 feet of film about the bombing, which was now available to the public from the US defense department. They made the movie ‘Prophecy’, which I brought to India.  This film formed a very important part of our movement. People like Shanks, Sanjay, Krishnan, Diba Siddiqi and others made an exhibition on nuclear disarmament. There were lots of talks and meetings as well. So this took away a lot of time – from the summer of 1984 to the end of the year. And elsewhere in the world string theory was exploding.

We had already formalized many things like how to construct a string moving on group manifold, Weyl anomaly cancellation putting restrictions on the group manifold etc.

SM: So you had the Wess-Zumino-Witten term?

SW: Yes because we had worked on the Nambu-Jona-Lasinio model. Just remove two dimensions and you get that.

SM: You had not read the non-Abelian bosonization paper?

SW: No. I was not aware of it to begin with in early 1984.

SM: You were looking for conformal theories?

SW: Yes conformal theories on group manifolds.

RG: Non-Abelian bosonization was 1983, I think.

SW: Where does he prove that the beta function is zero?

SM: With the Wess-Zumino-Witten term.

SW: Yes now I remember Witten’s paper. It was published sometime in 1984. We became aware of this paper and its importance after our work had progressed. But he doesn’t talk about string theory there.

RG: No no. It’s purely two-dimensional field theory.

SW: In the string theory framework you need the anomaly cancellation. So you start restricting the group manifold. All this works out nicely. I still remember that the anomaly term of the current algebra was a little tricky to derive.

SM: Yes one can easily get it wrong.

SW: Then one day Shanks had slipped a paper into my office. It said, ‘these are God’s rules.’ I still remember that – ‘God’s rules of how to regularize the current that gives the right answer.’

AD: Who was God?

SW: God knows who was God. [Laughs] You should ask him if he remembers.

I don’t remember in which paper of Witten…

RG: Certainly he talks about the beta function.

SW: Continuing the narrative, I knew about the work of Friedan on sigma models where conformal invariance leads to the Einstein equations in the absence of matter. But there was no time to put all of this together in the context of strings propagating in an arbitrary curved space. One reason could be time-sharing with the nuclear disarmament movement.

After this we, as a group, came back to just doing physics ... you gotta be strong in what you do and only then you can change a bit the world around you. As physicists we just needed to work and focus on physics. Spending too much time on disarmament was I think, an error. But, of course, during this excursion I learnt a lot about politics and how to manage people. It was a great learning experience. What was happening was that we physicists were amidst various factions of the Left. To begin with we did not know the political basis of why each faction presented a different way forward. But this was a great learning experience...but we lost a very big prize in physics...I think. However at a personal level I still continued my association with social and educational movements in India including the People’s Science Movement.

The project on conformal invariance in string theory became the PhD thesis of Sanjay Jain. There were already contributions to this project by Gautam Mandal.

RG: There was this first strings kind of meeting in Santa Barbara.

SW: Yes I gave a talk there.

RG: So was that the first real meeting?

SW: Yes. It was organized by Mike Green and David Gross.

SM: Which year was this?

SW: 1985.

RG: You and Ashoke are the two Indians in the proceedings of that meeting.

SW: Yes.

So this is how we started doing string theory – in India. After that a couple of years were spent on trying to ask the question – What are the principles of string theory?

SM: I wanted to ask – how did you learn the subject?

SW: Oh string theory, I knew from Chicago.

SM: But there were all these new developments – would you be reading the papers? Were there review articles?

AD: You learn on the job.

SW: Yes.

RG: Did you have some sort of group discussions?

SW:  No, not at that time. And this was a mistake even though we were very few.

RG: I guess Avinash had left.

AD: Only Spenta and students were doing string theory.

SW: Sunil Mukhi was also there by then. There was not too much of an overlap in the sense of directions of research. There could have been an overlap in writing down the classical string equations from sigma models. I was unable to put all our resources in people and physics together.

RG: He was also doing sigma models.

SW: Yes. Alvarez-Gaume, Friedman and Sunil had written an important paper on how to do background field perturbation theory and renormalization by expanding fields in sigma models using Riemann normal coordinates. All that couldn’t be put together and that was perhaps just the lack of time, lack of communication, and other situations in the department at TIFR. So this was a big miss, I think. And the paper on sigma models and classical string equations came from Ashoke Sen and Callan, Friedan, Martinec and Perry who also included the dilaton.

RG: I wanted to ask you about your attitude towards supersymmetry.

SW: You know a lot about me. That is a very loaded question. [Laughs]

RG: Supersymmetry before string theory, after string theory.

SW: I had a little problem with supersymmetry… a taste problem because of the supergravity papers... this was not for me. It is too complicated and I felt that nature couldn’t be like this. It’s great that we have type IIA and IIB string theories– they contain the organizing principles. So supersymmetry was fine, but all the complicated aspects of supergravity did not agree with me. I had heard a talk by Witten in Chicago at the American Mathematical Society meeting on supersymmetry and Morse theory. It was an incredibly beautiful talk and we used the ideas of supersymmetry many years later. And I will tell you about that. At that time we only knew about conformally invariant string theories. We knew about classical solutions of string theory. I did not like string field theory – I had heard talks on it by Kaku and Kikkawa who first constructed the bosonic string field theory. Sorry. That’s not my taste.

Perhaps there is an alternative way of understanding the field theory of strings, when you know the classical solutions. We know from Wilson that there is a space of flows connecting critical points and in 2-dims Zamolodchikov had proved his beautiful c-theorem. We assumed that the space of RG flows and fixed points –is the configuration space of string field theory. So we tried to understand this problem from the viewpoint of stochastic differential equations. I’ll tell you what happens here.

You know what stochastic equations are, of course. The renormalization group (RG) differential equations take you from one fixed point to another. The stochastic differential equation, obtained by adding a noise term to the RG equations, feels around like a rat in the space of flows, in the theory space. Therefore, it’s a good setting in order to understand the structure of two-dim field theories. We made a connection of Witten’s paper [on Morse theory] with the 2-dim `theory space’ and its critical points, using the c-function as a Morse function. Since you know the relevant operators at each [critical] point in theory space and suppose these relevant operators [instabilities] form a finite dimensional space, then the Morse index at the critical point is the Morse index. I knew from the lectures of Raoul Bott about Morse inequalities and under very special circumstances they become equalities; then the knowledge of critical points enable us to figure out the topology of the space because of the equality of the Morse and Poincare polynomials. All the Betti numbers are known. It’s amazing that for c<1 models, you know all the Betti numbers of the space of RG flows. So Sumit, Gautam and I wrote this up ... The paper is not well known but I really like this work.

RG: Which year did Sumit come back to TIFR?

SW: I don’t remember but I did make sure that he came back to TIFR. There was some difficulty in hiring him but it finally worked out and Sumit came around 1987.

SM: And when was Sunil hired as a faculty?

SW: He came as a postdoc and two years later…

AD: He was there before I left. So I think he must have joined around 1983.

RG: As a faculty?

AD: No as a postdoc.

SW: So after two years he joined as faculty.

SM: Did you play a role in his hiring?

SW: No. I was a Fellow then. So I wasn’t there in the departmental meeting. They just asked me for a write-up, discussing his papers, which I did. I also did the same for Sumit Das.

RG: Avinash, when did you come back?

AD: 1987.

RG: So already by 1987 there were four others.

AD: Yes there were four of us. Then students were there. Sanjay, Shanks and Gautam were also there already?

SW: Yes.

SM: Avinash, were you also working on string theory when you came back?

AD: Yes. I started working on string theory in SLAC. Along with this beautiful paper that came out on conformal invariance. We also had written one on how to construct vertex operators but in an old fashioned way. By writing down 2D gravity invariant operators – just explicitly constructing all of those. And we also worried about off-shell amplitudes. We had a whole section on this which Peskin said we shouldn’t include. He felt there was nothing like off-shell amplitudes. We found that you needed to retain the Liouville mode in order to write those amplitudes, which is what Ashoke is also telling us. But Peskin was very bothered about that. He actually was so vehemently against us writing that section that we dropped it and put it only as a remark in a footnote. In fact not only that – we had also found that you needed a Liouville type of a counter term, ∂² Φ, to remove divergences from the trace of stress tensor. At that point somehow we did not realize its significance.

SW: Now I will tell you a little bit about our work on Liouville theory and matrix models. The main question we continued to address is, `What is String theory?’. I remember Sumit and I were in Jaipur, attending one of the SERC schools. We were working on Liouville theory locked up in a room because of crickets. Studying the Distler-Kawai paper we realized – that the Liouville mode can be interpreted depending on the central charge as a space or time coordinate in string theory. We got very excited about that and wrote up a paper with Sachi Naik who was a postdoc at TIFR.

Why is Liouville theory important – it’s because it enforces conformal invariance when you integrate over 2-dim gravity! So that must be a good reason why conformal invariance is an important part of the principles of string theory. However we wanted to make sure that this was a correct idea. So with Avinash, Narain, Jayaraman and some others we reproduced the Veneziano amplitude exactly! We started with 25 scalar fields coupled to 2D gravity using Polyakov’s light cone gauge formalism and we got the Veneziano amplitude, including the measure. It was amazing. This was really the proof that at c=25 the Liouville mode emerges as a time coordinate in string theory.

AD: We wrote a paper with Sumit.

SW: Yes there was a follow up paper with Avinash and Sumit deriving general constraints on matter couplings dressed by 2-dim gravity. In this formulation there is no difference between critical and non-critical string theories. The couplings of the critical string theory were in one higher dimension that provided by the Liouville mode.

I think this whole conformal invariance business went on and on over many years. So that was the other obsession. After confinement, there was the question `what is string theory?’. What are the principles of string theory?

RG: You said the confinement problem was your main obsession earlier. And then it was string theory from the mid 80s. What was it about string theory that really gripped you?   

SW: The fact that it is ‘the theory of everything’... in physics. In some sense it gives you the framework to discuss particle physics and gravity. There was something unifying about it all. Conceptually unifying. Not maybe in terms of quantitative unification in which you can do a calculation. There is a notion of a conceptual unification which one should try to achieve. I think this was the attractive factor.

AD: Also at that time the atmosphere was such that people believed this was the theory that would solve everything. There was a lot of hype around what seemed like we had found the Holy Grail.

SM: And were particular people important for the hype?

SW: Witten was very convincing. But I think he was right since we are still working in string theory!

AD: Yes. I think we were very influenced by Witten.

SW: So we started working on matrix models. We organized ourselves in groups.

SM: This is in which year?

AD: 1989.

SW: Yes. Now Anirvan Sengupta had also joined.

SM: You said you started working on string theory in 1984 and then till 1989 you were trying to understand the structure of conformal invariance.

SW: Exactly. The whole idea was how to get away from string field theory. And it was not only I. When I was at the Institute for Advanced Study beginning the fall of 1990, one of the nice things was that Witten would many times come after lunch to my office and we would go for a walk. I would ask him about lots and lots of things. When he started working on his famous paper on string field theory, he said that he wanted to see it go away.

SM: Open string field theory?

SW: Yes. But he didn’t succeed and wrote a very nice paper on open string field theory.

During one of our walks I asked Witten why he wrote so many papers? He said that he had missed some things because he did not write them up. I have such a deep admiration for Witten; for his formidable abilities, his leadership and the poetic style of his papers. I asked him once whether he had read the Autobiographical Notes of Albert Einstein. He had not. So I told him that he should read them as they tell how Einstein relentlessly pursued fundamental questions of his times...over many years. In retrospect I feel very embarrassed that I said this to Witten. When he wrote his next few papers he would ask for my permission in jest!

SM: Sorry just one more point about this. Recently string field theory has found applications. Does that revise your view a little bit, or not?

SW: Of course it revises the view that it is useful. But whether I would work on it or be excited by it is another matter. For me, there are many other exciting problems in physics. Back to 1989 in TIFR: Avinash, Anirvan, Sumit and I wrote a paper, which was first to introduce double trace operators.

SM: Multi-trace operators in gauge theory?

RG:  In matrix models.

SW: Yes in matrix models. Tr (M²)²  operator and how to work with it and what its implications are for new critical phenomena in random surfaces. Then Igor Klebanov and his students took it up did very insightful work, and there was also a famous paper by Witten in the AdS avatar. It felt good that we did something good and useful at that time.

Now something interesting happened. We were doing Liouville theory, right? And Liouville theory is related to matrix models, right?

Now comes the story of the c=1 matrix model. That occupied me for many years. This is the time when we had the meeting at the Tata Institute on Modern Quantum Field Theory.

AD: Matrix models. This was the first big meeting.

SW: Yes, David Gross, Frank Wilczek, Volodya Kazakov, Antal Jevicki and others participated… 1990 January I think. This was before I went to the Institute for Advanced Study.

AD: They actually announced their results on the double-scaled matrix models for the first time in this conference.

SW: It was this second [Matrix] revolution, so to say.

RG: Migdal...?

SW: Yes papers by Gross and Migdal, Douglas and Shenker, Brezin and Kazakov discussed the double scaling limit of matrix models to describe continuum worldsheet of the string ... The 1990 meeting was good because we were also led to work on the c=1 models as they presented a possibility to discover the principles of non-perturbative string theory in 2-dims.

Subsequently there were several papers on the double scaling limit of matrix quantum mechanics. I was delighted to see that the double scaling limit in the matrix quantum mechanics model is taken exactly at the third order phase transition point, but there was no mention of my earlier work. This bothered me, but I did not say anything.

RG: Fits in well with your earlier interest.

SW: Yes. So I started working on the excitations of the double scaled c=1 model with Anirvan. The first thing we found was that the fermions were relativistic near the Fermi surface and the physical excitation was a massless boson. We derived the effective action including the effect of the wall, which leads to a cubic interaction. There were similar papers on the subject from the western world. One of them was from Polchinski and the other was the Das-Jevicki paper on the collective field theory formulation adapted for c=1 following the earlier work of Jevicki and Sakita. Around the  time I was in Chicago, Sakita and Jevicki had, expressed the matrix quantum mechanics in terms of density variables by a change of variable. I did not think that it was the exact boson representation of the c=1 matrix model. Today I know it is not, and it is the hydrodynamic limit.

In between there was work on the two-dimensional black hole. Why did that happen? Let me tell you about that. When I went to the Institute, Witten told me that Zeldovich was there the previous year and they had almost written a paper on how to solve the unitarity problem of black holes. That stuck in my head, I realized it was a very important problem. We had done matrix models; we had understood two-dimensional string theory in terms of the Liouville mode, so there better be a black hole here. So that thought was there. There was a seminar at Rutgers by Polchinski on the c=1 type of models. And he said that in two-dimensions the flat metric was the only solution, and I raised my hand. I mentioned in his talk that this is not right if there is a zero of the dilaton field, because that’s the signature of the black hole...we [Gautam, Anirvan and I] knew that at that point. And then I told Gautam and Anirvan, drop everything. Let’s find this black hole solution. Anirvan used a gauge in which the dilaton was linear and found the black hole solution. Gautam and I worked out the solution in the conformal gauge. We did this as we were driving on Route 27 in between Rutgers and Princeton.

SM: Also known as Nassau Street within Princeton.

SW: At that time I had an injured leg and I was at home all the time. I remember Sunil Mukhi visited me at home and he told me that there was a lot of excitement in the Institute about Witten finding the black hole solution. I went and told Witten about what we had done. I used to sit in one of these ground floor offices opposite the mailboxes. Witten would inquire now and then about the progress of our paper. As you know when he wrote his famous paper, there was a big splash. We wrote our paper before his and he quoted us. I asked him point blank one day, ‘do you think we couldn’t have done it?’ Our motivation was matrix model and its natural connection with the Liouville mode that contributes the spatial dimension of 2-dim string theory. If the black hole solution is understood in the matrix model we could solve the unitarity problem. He said, ‘no no it’s not like that.’ I still remember Witten’s seminar afterwards and there was no place to sit in the hall at the Institute. Anyway, this is about the two-dimensional black holes and the motivation behind it.

As I mentioned before we were trying to understand the microscopic basis of the c=1 matrix model in order to gain insight at some of the principles of string theory. Polyakov had found an infinite spectrum of discrete states in 2-dim string theory. It is a very beautiful piece of work. How can one understand this from the matrix models? One clue came from the W-infinity symmetry algebra and its conserved charges that we had discovered in the matrix model. Avan and Jevicki also arrived at similar results but in the classical limit. Gautam and I told Witten about this result and he was hazzar excited. Then we continued working on the problem with Avinash and Sumit who were in India. And even though the Internet was there, the communication was not so great. We were trying to understand the discrete states of Polyakov in terms of the W-charges. It took many months of work before we had a reasonable understanding of these states in the matrix model. In the meanwhile Witten wrote his paper on the ground ring of the c=1 matrix model and he did acknowledge us for discussions.

We worked on two-dimensional string theory and matrix models for a long time, trying to find signature of the black hole solution we had discovered in the matrix model. But this did not work out.

We also constructed the map from the matrix model to 2-dim string theory, to which Avinash made an enormous contribution. It is a highly non-linear map.

SM: This is with the leg pole factors?

SW: Yes.

SM: This is still not completely understood, right? Experimentally you know what the map is but the principle behind the map is still unknown.

SW: It is a recipe that you give.

SM: Do you think this is an important problem for the next generation?

SW: I think so. Because if you can solve this problem in AdS/CFT then you will (I think) understand the variables of space-time and also the internal degrees of the freedom of the black hole. We have a good understanding of finite temperature field theories and the plasma ball configuration is a holographic image of the black hole.

SM: What I feel here is that often we tend to hide behind AdS/CFT, hide behind the fact that we can’t solve the field theory. We don’t understand AdS/CFT partly because it’s strong coupling but that’s bullshit, I think. Because in this one example where you can solve both sides completely, you don’t understand the logic for the map? That makes it clear that you haven’t understood something that is not a technical issue but a principle.

SW: Absolutely. I have some thoughts on this, but maybe this is not the time to discuss this further.

AD: Also in this case the map is written down because you know the other side.

SM:  Exactly. But here you have this rich resource of having an example where both sides are solved, sounds like you should be able to mine that to discover the principle.

SW: Gautam, Anirvan and I had computed the boson S-matrix from the matrix model. You don’t find the discrete states in the intermediate states! So, yes, we don’t understand the map. I completely agree with you. These states are created by the charges of the W-algebra but we do not see them in the S-matrix! I agree with Shiraz, this is a very important problem to solve if you want to figure out the emergence of space-time and the internal degrees of black holes. We have discussed this many times.

Okay so this brings us to the time when I got fed up of string theory. Nothing was working [for us].

 

Physics in India and the Building of String Theory…

RG: Can I ask one question? By then TIFR had a large…

SW: Oh I see! You want to know how the string theorists got hired at TIFR?

SM: Yes, like Ashoke.

RG: And there was a growing international visibility... you mentioned the 1989 conference. Can you say a little bit about that?

SW: Yes. I knew I had to bring Sumit Das back because I knew him well and had a very high opinion of him.

I was not part of the decision-making as I was a fellow. The fellows were not part of the ‘group committee’. Sumit was the first person I wanted to attract back. TIFR hired Avinash also... for all the work he had done in perturbative QCD. Then after some time we also hired Gautam because he was excellent and I knew that we needed a critical size to begin with. I had some difficulty with the induction of Gautam because he was my student. I knew from my Chicago days that hiring your own students is not something you do. But our circumstances were very different.

I visited Sumit in Fermilab. Both Sumit and Ashoke were post-docs there. I met Ashoke and spoke to him at length about coming to TIFR. By then he had already done some very beautiful work. I still remember - he was sitting in his office and his desk was almost empty. At that time there was the general impression that getting a job at the Tata institute was difficult. He said, ‘Now I will have to work harder.’ This was the first conversation I had with Ashoke Sen. I really urged him and I told Sumit as well to urge him to join TIFR. Sumit knew him very well – they were college friends. So it started like that. Then at the Institute [IAS], I overlapped with Sandip Trivedi who was a postdoc at that time. Atish Dabholkar was a postdoc at nearby Rutgers University. I urged both of them to come back [to India and TIFR]. I also met Shubha Tole with Sandip and encouraged her too to return to India after her post-doc.

This is how it was and I think we got really lucky. It was our good luck that people were working on string theory and related problems, and were interested in coming back. Then the next hire was Shiraz. He was in Harvard then. And I was in correspondence with Harvard. Shobo had asked me to do this. The correspondence was basically with Andy Strominger. They didn’t want to let him go. Then there was the issue of a joint appointment, and while Harvard was agreeable we had to get it approved at TIFR. We managed that. I knew more or less that once this guy is here he will not go back. I had that intuitive feeling somehow, just by talking to him. True, right?

SM: Yes true.

SW: Shiraz, you and our colleagues in Mumbai have a similar challenge sustaining the string theory activity. Shiraz has created all these incredible students – two of his students are our faculty [at ICTS]. This is an amazing contribution. Creating the ICTS has temporarily depleted the home institution. However this was never on my mind because the ICTS has separate and distinctly new missions.

Anyway, coming back to physics, after working hard on matrix models which did not yield the secrets of black holes I got fed up of string theory and started working on complex systems. Physics discovers simple laws but their manifestations are very complicated. We worked in this area for about two years.

SM: Where did this come from? Was it something you were always interested in? Or were there new developments?

SW: No. This had its seeds at the University of Chicago. The fact that Nambu, Leo and Chandra had made contributions to so many diverse areas impressed on me the fact that there is so much unity in what seem disparate areas of science. Leo even spent some time on urban planning. There was also Jack Cowan at Chicago, who worked on questions of biology. For me biology is an extension of physics except it is a much more complicated system that exhibits among other things reproduction. The living state is something we have to understand as physicists.

So I thought it was a great idea to work on something different. Biological systems are too complicated so we began work on the simplest system that exhibits complex behavior: cellular automata. We explored complex behavior at the edge of order and chaos that exhibits complex pattern formation and long-lived dynamical activity. We started working on these dynamical systems and most of the calculations were done numerically. My student Porus Lakdawala had a lot of insight in this area. We found the surprising result that the system under study can access ordered, chaotic or complex behaviour, provided one tunes the initial conditions. Few years later I got a letter from some mathematicians from Chicago that they had actually proved this rigorously. Our work was numerical and our finding could be rigorously established.

So this [diversion] was for about two years and Porus wrote his PhD thesis on some work that he did by himself, “On the computational complexity of symbolic dynamics at the onset of chaos”. Porus is very deep thinking and philosophical ...but he didn’t like string theory at all.     

At the end of two years I was facing a problem– who am I in this subject? I also felt that I did not really have a solid background in computation theory or biology to make a mark in the subject. Fortunately by this time wonderful things were beginning to happen in string theory due to the works of Polchinski, Strominger and Vafa.

SM: So what fraction of the TIFR was doing the complex systems? Ashoke kept doing string theory, right?

SW: Yes, Ashoke did.

SM: What about Sumit?

SW: I think Sumit had left already. Or was he around? I can’t remember that.

AD: Sumit was around. He had these collaborations that he was working on – with Jevicki.

SW: Yes that’s right.

AD: He had veered off into a different direction.

SM: Inspired by matrix models.

SW: Yes. And I think Sunil Mukhi was working on topics like topological strings.

SW:  Biology was something that I always wanted to do, even as an undergraduate. In St Xavier’s College I had studied Watson and Crick’s book and I used to visit the TIFR biology department and have lots of discussions with the biologists about how relevant physics is for what they were doing. There used to be big debates about this. I was always interested in understanding biology from the viewpoint of physics. And this time seemed like a good opportunity. Both my students Anirvan and Sanjay – work among other things on biology inspired questions. They arrived at doing so on their own.

SM: What does Porus do?

SW: He works in the Oracle Corporation in California.

RG: So with all these students you had, what was the interaction like?

SW: My students were all friends. Friends to the extent that one student of mine also punched me.  [Laughter] Anirvan – he got all excited. We were at Parade Platz in Zurich and discussing the effective action of the c=1 matrix model. He got angry with me. So he just gave me a punch. Of course I returned it many months later. All my students were my friends and it was like a family.

RG: It must have been very satisfying to mentor these very good people?

SW: Oh yes. Most of the little we accomplished wouldn’t have been possible if these people were not there. I worked closely with all my students. We didn’t have very good post docs then, with the exception of David Tong, Allan Adams and Matt Headrick.

I just wanted to finish speaking about the physics first. So what were we talking about? Yes the work of Polchinski, Strominger and Vafa.

Strominger and Vafa made a decisive leap when they calculated the entropy of an extremal black hole by counting states and using Boltzmann’s formula. This was a big development: the new degrees of freedom that Polchinski discussed, D-branes – account for black hole entropy! Even today if you ask me what is one of the most important achievements of string theory it would be the discovery of the new stuff (D-branes) and how the new stuff accounts for black hole entropy. It was unbelievable. It changed the direction of the subject and brought black holes back to centre stage.

We started further work on the modeling of black holes by D-branes. Gautam came to my office and said that now that there is a microscopic theory we could solve the problem of the asymmetry of time reversal and black holes. I said yes. So we tried to model the Hawking radiation using a variant of the Strominger-Vafa model to describe a non-extremal black hole. That’s how the three of us (Gautam, Avinash and I) started working on trying to model Hawking radiation. As Strominger-Vafa in this calculation dealt with the ground state of an extremal black hole, the question was how to model the interaction between an external particle like the graviton and the brane bound state? So we had to study that. There was work done by Klebanov on the interactions of closed strings with branes. All that had to be understood.

The first calculation we did was in classical general relativity. When you scatter an s-wave off the black hole of Strominger and Vafa what is the cross section at zero frequency. We found that it was exactly equal to the area of the black hole horizon.

SM: You were the first to show that?

SW: Yes the first, in this model. Then we tried to reproduce this result in the D-brane model. We could reproduce the answer except for a coefficient that we couldn’t fix from first principles. So we wrote our paper without fixing this constant.

When we sent our paper to the arXiv, I received a mail from a certain Juan Maldacena at Princeton University. I didn’t know who he was. He wrote that they were doing similar things.

SW: Then I went on a sabbatical to CERN. My main focus for many years was how to obtain Hawking’s formula entirely within the D-brane model. This was before Maldacena’s groundbreaking work on AdS/CFT. With Fawad Hassan, who was a postdoc at CERN, I spent a lot of time on the D1-D5 brane system and the associated two-dimensional gauge theory with appropriate D-terms. If you set the D-terms to zero you get the moduli space of this theory that describes its low energy modes. Later on we learnt that this moduli space was related to the moduli space of a five-dimensional gauge theory. I persisted with this work because I was really keen on deriving the formula for Hawking radiation from first principles. There was a conference in ICTP where I gave a talk on this. At this meeting Maldacena also gave a talk.

SM: Which year was this?

SW: I don’t remember now.

SM: Was this before his paper?

SW: Yes. I had a short discussion with him. I spent a lot of time trying to make solid the gauge theory-gravity correspondence so that we can compute the Hawking radiation coefficient. This issue we ultimately understood in a series of papers with Gautam and Justin using the AdS₃/CFT₂ correspondence. You have to fix the normalization of the 2-point function in the AdS/CFT correspondence in the sector that does not contain the black hole. This in turn determines the coefficient in the Hawking radiation formula.  This important result is part of Justin David’s PhD thesis.

As you say, we cannot prove the precise correspondence. Most people don’t seem to care about this ... but this has always bothered me very much. This is why I spent many years trying to understand this coefficient.

After the D1-D5 system and the black hole project I spent some years working on the unitary matrix model that describes the N=4 gauge theory at finite temperature and reproduces the most important qualitative features of the tunneling between thermal AdS and the big black hole. We also proposed a correspondence of the small black hole – string transition with the large N transition in the gauge theory. This project formed the PhD thesis of Pallab Basu.

After some work on hydrodynamics in 2-dims with Justin David and his students, I started working on hydrodynamics with Shiraz, Sandip, Sayantani and Loganayagam. I am fascinated by hydrodynamics. For the c=1 matrix models collective field theory is the hydrodynamic approximation. We wrote a couple of papers.  One was trying to make a dent in the most important problem of hydrodynamics – turbulence. That was our ambition and outlook at that time. That’s why we did the stirred fluid-gravity correspondence.

Then came the Navier-Stokes equations where we showed that there is a universal scaling limit of any relativistic hydrodynamics that gives the non-relativistic Navier-Stokes equations. This correspondence also throws light on the symmetries of the Navier-Stokes equations. All that was very satisfactory. But the problem of turbulence is still at large.

In all these works I was working with super-smart students Sayantani and Loganayagam.

SM: Yes Loganayagam was the hidden author on that paper. He even submitted the paper on the arXiv but refused to sign his name on it. I couldn’t understand why.

AD: Why?

SM: I think he felt he hadn’t done enough work on it. But it’s very hard to know with Loga.

SW: Yes, you can’t figure out.

So that was the fluid dynamics work. Then came the Chern-Simons project with Shiraz, Sandip and their students and collaborators. I was working on it when the ICTS was being created. This project sustained me. I was working doubly hard, doing both things. Without this group at the Tata Institute and Shiraz, I don’t know what the situation would have been like because continuing to work in physics was very important for me in order to go on working for the ICTS.

I think we did some nice work. Missed some important points. I was hazzar thrilled actually. It was immense fun working with Shiraz. The most gratifying part of my stay at the Tata Institute, the last part, was that. Thank you.

SM: Thank you.

SW: No really. I wanted to say it at some point. And it happened because our tastes match. In a sense our tastes are very similar, except that he likes supersymmetry a bit more. [Laughter]. It’s great that it worked out that way. It was a lucky thing. All this very beautiful work on scattering theory – that was amazing, right?

SM: Yes amazing.

SW: You think you know about some problem but actually you know little [referring to the Aharonov-Bohm effect.]

SM: It’s still largely unknown in the world. But it will come.

SW: I was thinking about this article I wrote on the talk I gave at the Salam memorial meeting. I haven’t put it up on the arXiv. I was wondering whether we should write a review based on that. What do you think?

SM: Yes, we should.

SW: We should do this. The template is there and you are so fast that we will have the review within… [Laughter]

I will tell you one incident about Shiraz. This is concerning our paper on Chern-Simons matter theory on S² x S¹, right? Here there is a new type of matrix model in which the density of eigenvalues is bounded reflecting the discreteness of the Chern-Simons fluxes. There was a difficult integral equation to be solved, along similar lines as the integral equation of the unitary matrix model, which I had done a while ago in Chicago. But I could not have done this new problem as fast. Within a day the problem was solved. The whole solution was there. Shiraz I think is just incredible. We are very happy that we have you.

This guy [Rajesh] just wouldn’t come to us.

SM: Why not Rajesh?

RG: I will tell you when I am 65. [Laughter]

SW: I may not be around. This is not fair, you must say it now.

SM: Rajesh used to say all this about being in the heart of India, the Ganga. But now he has moved to Bangalore.

SW: Cauvery. Now he is near the Cauvery.

RG: So from the time when you came and till the time you are talking about, the string theory group had a certain visibility in the world. So how do you see this evolution? Is that a model for how other areas, groups could build?

SW: Yes certainly.

In retrospect I can say that while building institutions you have to be mindful about the times and about the yardstick for induction. If your bar is too high then there is a problem. The problem is that you cannot be sure, beyond a point, about the potential of people. Many in our group at the Tata Institute, did their best work while at the Tata Institute. So you need to have a good sense of what the person may do in the future. Even at ICTS, which we will talk about later, it has been a nightmare building the faculty.

The issue of travel is very important – going out and talking to people about the science you are doing in India and urging potential faculty to return. I think the other groups did not do enough of that. I will give you an instance that made an impression on me. In 1982, I was sharing a long train ride from Saclay to Paris with Ludwig Faddeev. We were talking and he said, ‘every summer I come out to tell the world what we are doing in Leningrad.’ That made an impression on me. That he went around telling the world what they were doing in Leningrad made them very visible. As a student I still remember his Loeb lectures at Harvard. My advisor would never accept a student without a test. So he asked me to read the Faddeev-Takhtajan paper on the Sine-Gordon equation. I don’t know if you have studied that paper, but it is an extremely difficult paper for a beginning graduate student...the inverse scattering method, the Gelfand-Levitan-Marchenko integral equation etc. I just didn’t know what to do. I didn’t know how I was going to study all this and report to him. My friend Rashid Shaikh was a student at MIT, so I went there. I attended the Harvard lectures they were very inspiring. I learnt a lot from them. There I witnessed the confidence with which Faddeev was handling Sidney Coleman who was asking many questions. Faddeev’s example influenced me a lot– that you go out every summer telling people in the best places what you are doing back home. This is how [I think] the postdoc position for Avinash at SLAC came about. I went there to give a talk and told Peskin about Avinash. I also told him that he wasn’t my student. But then he said, ‘it doesn’t matter that he is not your student. You have shown him the right way.’

So the first great success of our work at the Tata Institute was Avinash going to Stanford as a postdoc. Both the work we did and that I travelled telling people what we did at TIFR helped in this. Before Avinash most theory group students went to Europe for their postdoc.

SM: In any subject?

SW: Yes as far as I remember. Please correct me if I am wrong.

AD: I don’t know this.

RG: No he is talking about post docs.