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Home , Gary Horowitz, Greg Moore (physicist), Michael Dine, Nathan Seiberg, Stephen Shenker

Round Table Talk: Conversation with

Nathan Seiberg Professor, the School of Natural Sciences, The Institute for Advanced Study Hirosi Ooguri Kavli IPMU Principal Investigator Yuji Tachikawa Kavli IPMU Professor

Ooguri: Over the past few decades, there have been remarkable developments in quantum eld theory and theory, and you have made signi cant contributions to them. There are many ideas and techniques that have been named Hirosi Ooguri Nathan Seiberg Yuji Tachikawa after you, such as the Seiberg duality in 4d N=1 theories, the two of you, the Director, the rest of about . You started Seiberg-Witten solutions to 4d N=2 the faculty and postdocs, and the to work on supersymmetry almost theories, the Seiberg-Witten map administrative staff have gone out immediately or maybe a year after of noncommutative gauge theories, of their way to help me and to make you went to the Institute, is that right? the Seiberg bound in the Liouville the visit successful and productive – Seiberg: Almost immediately. I theory, the Moore-Seiberg equations it is quite amazing. I don’t remember remember studying supersymmetry in conformal eld theory, the Afeck- being treated like this, so I’m very during the 1982/83 Christmas break. Dine-Seiberg superpotential, the thankful and embarrassed. Ooguri: So, you changed the direction Intriligator-Seiberg-Shih metastable Ooguri: Thank you for your kind of your research completely after supersymmetry breaking, and many words. arriving the Institute. I understand more. Each one of them has marked You received your Ph.D. at the that, at the Weizmann, you were important steps in our progress. Weizmann Institute in 1982 and working on model building, Today, we would like to look back immediately went to the Institute something related to . on the history and hear from you for Advanced Study in Princeton as a Seiberg: Yes, it was not successful. So how you made these discoveries postdoc. when I moved to my postdoc position, and your perspective on the future Seiberg: That’s right, I came there for I thought I should change direction development of quantum eld theory my postdoc. and I thought that supersymmetry and . Ooguri: That was before my time. I was interesting. Seiberg: Before we start, I would became a graduate student in 1984, Ooguri: What did you nd most like to thank you very much for your and I remember reading your papers interesting about supersymmetry at invitation and for your kind words. intensely after the so-called rst that time? The hospitality at Kavli IPMU during superstring revolution since I wanted Seiberg: Supersymmetry looked like my visit here has been fantastic. The to catch up with what was known an interesting intellectual structure,

14 Kavli IPMU News No. 34 June 2016 which might also be relevant for paper with Anne about the analysis this was the biggest surprise. These phenomenology. had of the at directions of the theory are quantum eld theories with been working on supersymmetry and we argued that a certain several ground states. before and he encouraged me to superpotential should be generated Ooguri: Continuously many ground learn it. He recommended that I study there. Our analysis was based on states parameterized by the moduli the Wess and Bagger book, which consistency conditions and the space. was still in preprint form. (Julius Wess symmetries of the problem, but we Seiberg: For me that was shocking. had just completed a series of talks did not prove that this superpotential Ooguri: So, some of the very at Princeton the year before. And is indeed generated. important concepts in supersymmetric Jonathan Bagger, who was a student theory appeared within a year or so. at the time, took notes, which Supersymmetry and Seiberg: There were precursors of eventually became the famous book.) Non-Renormalization of that in previous papers, primarily Ooguri: Was Michael (Dine) also a Superpotential several papers by postdoc there? Seiberg: Then Anne left and we and in particular, a paper by Ian Seiberg: Michael was a 5-year started working with Ian Afeck. Afeck, Jeffrey Harvey and Edward member at IAS and I came in as a That summer we wrote a paper Witten, which had analyzed the same fresh postdoc. He took me under his showing that in some circumstances problem in 2+1 dimensions. wings and became my mentor. He this superpotential is generated by We also spent some time trying had a huge impact on me. Our rst . This was very surprising to build models of particle physics project was about the dynamics of at that time because people had phenomenology. So we were primarily supersymmetric QCD. It’s hard to believed that the non-renormalization interested in breaking supersymmetry. imagine now how confusing it was at theorem was exact and was also true The theories with a of the time. non-perturbatively. vacua were a nuisance. They could Tachikawa: Then came your paper Ooguri: Were you convinced that the not be used for that purpose. with Ian Afeck and Dine on standard argument was wrong? Then in the summer of 1984 supersymmetry breaking. Seiberg: Most of the previous Michael Green and John Schwarz Seiberg: The rst paper we wrote was arguments for the non- wrote their revolutionary paper and with Anne Davis, where we wrote the renormalization theorem were based the physics world changed overnight. superpotential based on symmetries. on Feynman diagrams and were Even that was not obvious at that intrinsically perturbative. They did not First Superstring Revolution time. Crucial earlier work on the apply to instantons. I remember that in 1984 subject had been done by Edward the computation itself took Ooguri: When did you hear about it? Witten. maybe a week. Then it took another Seiberg: I heard about it in late Ooguri: Are you talking about two months to go through all the August or early September. Everybody Witten’s paper on the index? arguments in the literature and to was talking about this fantastic Seiberg: There were two papers. debug them. breakthrough, but none of us, the One about the index and the other So we wrote a short letter and then postdocs, had any idea what the was called dynamical supersymmetry we wrote a longer paper deriving the breakthrough was about. There was breaking. I remember studying superpotential… some mysterious theory, string theory these papers very carefully because Tachikawa: This is the Afeck-Dine- that we had never heard about. This they were full of wonderful things. Seiberg superpotential. was something that the older people In particular, the behavior of Seiberg: We showed that, depending had worked on and abandoned. They Round supersymmetric Quantum Chromo on the number of avors and colors, thought“, This was a failed attempt Table Dynamics with massive quarks was it is generated by instantons or and younger people should not learn analyzed. However, at the time there by gluino condensation. For more about it.” was no coherent picture about the avors, no superpotential is generated Ian Afeck left for a year in Paris, behavior of the theory when the and the vacuum degeneracy of the and Michael Dine and I had to decide, quark masses vanish. We wrote a massless theory is not lifted. For me, “Are we going to pursue our work

15 on supersymmetric gauge theories, had developed, such as your work on found using microscopic () or are we going to study this new worldsheet instanton. reasoning turned out to have simple thing?” And we decided to study Seiberg: Sure, that is true, without macroscopic explanations. string theory. That fall David Gross doubt. In particular, thinking about In fact, this line of investigation gave a fantastic string theory course moduli space of vacua, looking for helped uncover a number of at , mostly in non-perturbative effects that can lift interesting and subtle effects in order to educate the young people. the degeneracy, and controlling them the worldsheet technology. In The course was very popular and it by holomorphy were central in our hindsight, the main tool we used was was attended by all the postdocs at work on string theory. the constraints from holomorphy the university, all the postdocs at the A typical interesting example of of the spacetime superpotential, Institute, all the students, and many that occurs in various instanton which is associated with spacetime faculty members. It was given in a computations. There the real part of supersymmetry. It is not manifest huge lecture hall. the answer, which is the instanton in the worldsheet computations Tachikawa: Was it before the action, is combined with an imaginary and therefore, it leads to powerful heterotic string was constructed? part, which is the topological charge, constraints on the allowed answers. Seiberg: During that fall the heterotic to give a holomorphic answer. This Ooguri: I think one of your papers string was constructed, Calabi-Yau guarantees that the instanton can had a title which actually expressed compacti cations were discovered, contribute to the superpotential. At that point of view“: Microscopic and many other major developments that time, it looked like a complete knowledge from macroscopic physics happened. Many of us felt very magic. Afeck, Harvey, and Witten in string theory.” dif cult to keep up. As we were noticed it in 2+1 dimensional eld This was the opposite of what learning the basic material, like the theories, Afeck, Dine, and I saw it in most of the other people were doing, bosonic string, many new discoveries 3+1 dimensional eld theories, and to try to derive macroscopic results took place. then the same thing happened in from a microscopic description. You Tachikawa: Did David Gross cover all worldsheet instanton contributions advocated that generic properties of those latest developments during to the spacetime superpotential in of the low-energy effective theory the course? string theory. Every time we saw that, can help elucidate some of the Seiberg: His course was mostly about it looked like a miraculous consistency microscopic properties. the bosonic string. condition, and we did not know a Seiberg: That's right because some Tachikawa: Were notes of this course deep underlying reason why this of the symmetries are manifest ever published in some form? That occurred. Of course, today this is in the low-energy theory, but are might also be an interesting historical completely understood. not manifest in the short-distance document. During that time Michael and I tried computation. An example of that Seiberg: I think David followed the to understand various phenomena is the string non-renormalization available reviews at the time. Later, in string theory from a macroscopic theorem. The original proof was when I was at the Weizmann Institute perspective. We asked ourselves how based on worldsheet methods, but it in and then at Rutgers, I taught to describe them from a perspective was not sensitive enough to detect string theory and I used my notes of a low-energy observer. And we some subtleties associated with from that course, expanded them and tried to summarize many results contact terms. Michael and I found updated them. obtained by worldsheet techniques another proof, which was based on During the following years Michael in a spacetime effective action the holomorphy of the spacetime Dine and I continued to collaborate and in particular, in the spacetime superpotential. That macroscopic on string theory. superpotential. Our motivation was proof was totally conceptual and Ooguri: Even though you put your to see to what extent string theory very elementary. And it pointed to work on supersymmetry aside, some can lead to phenomena that a low- special situations where nontrivial of your works in string theory in energy observer would be surprised renormalization could take place. This the following few years were clearly by. If I recall correctly, many of the was discussed in a later paper with taking advantage of tools that you “miraculous” results that people had Michael Dine and Edward Witten.

16 Kavli IPMU News No. 34 June 2016 This was puzzling because the Seiberg: They had a picture in terms Although we had a clear and worldsheet methods suggested that of a certain vector bundle over consistent structure, at the time there are no such special situations. A Riemann surfaces, which at that time we had no idea what the proper detailed analysis of this case has shed I did not understand at all. I didn't mathematical setting for it was. Useful new light on the worldsheet methods even see what they had in mind conversations with David Kazhdan and uncovered the signi cance or where they were heading. Then and Pierre Deligne pointed us to the of contact terms, which had been another piece of this story came with connection to category theory. Of ignored in earlier work. the work of Erik Verlinde. He visited course, at that point in time we did By having a simpler proof, you Princeton and he gave a talk on not know anything about category sometimes understand what really what is known today as the Verlinde theory. I remember very vividly how goes into it. If you have something algebra and the Verlinde Formula. He I looked at the book that Kazhdan very complicated with a lot of moving described the fusion rules of a rational recommended and I said“ What am I parts and it's not quite clear what is conformal eld theory in terms of going to do with this?” And I left for and what is not essential, it's hard to integers satisfying certain properties the day. Fortunately, I was working see how to go around a proof. But and he suggested that the modular with Greg... The following morning, with a simple proof, it was clear. This transformation matrix S should he gave me a beautiful lecture was another example of how the diagonalize them. That was stunning. summarizing all we needed to know low-energy description points to a I still do not understand how he got from that book. loophole. this fantastic insight. Ooguri: That’s typical of Greg. So, with Greg Moore, we tried to That was before Witten's Paper on Conformal Field Theories and understand Verlinde’s work. After the Jones polynomial. I remember Topological Field Theories making some progress we came reading your papers on the Ooguri: Some of your works also across papers by Yukihiro Kanie classi cation of rational conformal had very deep and broad impacts and Akihiro Tsuchiya, which were eld theories just before I came to the in mathematics, such as your very mathematical. (Yesterday I was Institute. classi cation of conformal eld theory very pleased to meet Tsuchiya for Seiberg: I don’t remember all the and polynomial equations, which the rst time.) But we managed to details, but I think there were several characterize fusion and modular extract from these papers some different lines of investigation of invariance, with Gregory Moore. simple concepts that we could seemingly unrelated problems, These works also had impacts on use. We studied the properties of which came together. One of them physics, for example in topological the transformations of conformal was rational conformal eld theory, phases in condensed matter physics. blocks in a rational conformal eld starting with Friedan and Shenker, So, deep mathematical structures that theory and showed that they are Verlinde, and our work. Witten was came out from quantum eld theory characterized by a nite set of data. interested in the Jones polynomials. have had broad applications. Furthermore, that data had to satisfy We wrote a series of papers in the Your work with Greg on the a number of highly constraining spring and summer of 1988. Witten’s classi cation of conformal eld theory consistency conditions, which were paper came out in the fall of 88. appeared just before I arrived at the given by some polynomial equations. Ooguri: Were there interactions Institute. Could you tell us how this In fact, these conditions were so over- between the two directions of work came about? constraining that it looked surprising research? Seiberg: From my perspective it that they have any solutions. Seiberg: I do not know to what extent started with the work of Daniel One outcome of these polynomial Witten was inuenced by our work. Round Friedan and Stephen Shenker. equations was that we could prove He de nitely referred to it in his paper. Table (Greg Moore had related ideas Verlinde’s conjecture about the But it is clear that his point of view, independently.) relation between the fusion rules based on a three-dimensional picture Ooguri: They advocated the idea and the modular matrix S. I am still was broader, more general and had of the space of all conformal eld amazed by his intuition. How did he deeper insights. We had a sequence theories. come up with this conjecture? of transformations in two dimensions,

17 of vacuum in the Liouville theory is very confusing, for example. There are states which do not belong to Hilbert Space but still have roles in the theory. You put everything in a meaningful package. Seiberg: Thank you. Ooguri: No, I'm not just complimenting you. I just wanted to hear how you did it. Seiberg: Well, it was very confusing and I remember asking myself these questions. Earlier Knizhnik, Polyakov, and Zamolodchikov wrote a beautiful paper about two-dimensional gravity. but we did not realize that we should moved to Yale and there he did what Immediately afterwards, David and have thought of it as a theory in three I think is the nicest application of that Distler and Kawai gave a Liouville dimensions. body of work. Together with Nicholas interpretation of their results. Then Ooguri: In fact, when Witten Read they found the Moore-Read Douglas and Shenker, and Brezin calculated Wilson loop expectation state. and Kazakov, and Gross and Migdal values, he reduced it to the two- used a matrix model to describe two- dimensional problem and used the dimensional gravity and their answers Clarifying the Liouville Theory modular transformation and fusion were extremely simple and beautiful. language. Ooguri: It has had a direct application In view of that I felt that even though Seiberg: But he also used certain to condensed matter physics. Liouville theory might not satisfy all intrinsically three-dimensional Another thing that I wanted to the standard axioms of a conformal operations. And, of course, he also ask you about in this period, before eld theory, it should still be a sensible had a beautiful description of it in the second superstring revolution, theory. This motivated me to look into terms of a Chern-Simons Lagrangian. is about your work on the Liouville it in detail. Ooguri: But, nowadays this is used for theory. This was a very confusing In addition to the data from the theories without Lagrangians. So it’s subject for many years, and many matrix model there was also a huge coming back to where you were. wrong things had been said about it. literature on the semi-classical Liouville Seiberg: Yes, but you still have I remember, you came to Kyoto and theory. There were many things to assume that there is a three- gave a set of lectures solving many that had to work and so I just tried dimensional Lorentz invariant and of the confusions in Liouville theory, to make it work. Then I continued even topologically invariant theory putting everything in order. You following on that with Greg – we had underlying the whole structure. threw out many wrong statements, a very productive time trying to make In practice, when you compute and what you picked turned out to be this connection between the matrix something, it is not that different from all correct. How did you do that? model and Liouville theory more the computations that we did. But Seiberg: It bothered me that this precise. we didn’t have the better conceptual conformal eld theory does not satisfy Of course, since then our picture. the general axioms of a conformal understanding of the theory was Then we tried to complete the eld theory. So it was natural to ask completely transformed by the dictionary between our earlier work how to relax the axioms such that a work of Dorn and Otto, and the on rational conformal eld theory and coherent picture emerges. Zamolodchikov brothers and others Witten’s Chern-Simons picture. That Ooguri: The Liouville theory is non- who found the exact solution of took another year. After that, Greg standard in many ways. The notion Liouville theory.

18 Kavli IPMU News No. 34 June 2016 Dine, which were very stimulating Murray Gell-Mann described it as Power of Holomorphy for me. We started talking and the Totalitarian Principle“: Everything Ooguri: After that, you went back to eventually we wrote a paper about not forbidden is compulsory.” ’t the supersymmetric eld theory in the relation between R-symmetry Hooft described the same thing as the early 1990s – maybe a couple of and supersymmetry breaking. (Some “naturalness” – parameters take years before the second superstring people refer to it as the Nelson- natural generic values unless there is revolution. Did you foresee anything Seiberg theorem.) This followed an a good reason, e.g. a symmetry, not coming? I am asking this since observation Ian, Michael, and I had to do that. But then, supersymmetric what you did in these few years in made 10 years earlier, and it turned theories seemed to violate that the early 1990s on supersymmetry it into a more concrete and much principle. The superpotential is turned out to play essential roles clearer principle. not renormalized and can be non- in the developments of the second Ooguri: This was the beginning of the generic. This looked strange and revolution. What motivated you to modern approach to supersymmetric the cancellations behind it seemed come back to the supersymmetric eld theory. miraculous. Then, when it was realized eld theory? Seiberg: This was one element. The that non-perturbative effects violate Seiberg: I was working on conformal second element was inuenced by the perturbative non-renormalization eld theory and two-dimensional my work with Yossi Nir, where we theorem, it became clear that we gravity, and I felt that it was time to used spurions and the fact that the need an organizing principle. In change. So I worked with Yossi Nir on superpotential had to be holomorphic other words, to what extent are the model building – theories of quark in them. genericity properties of quantum and squark masses. And then I learned Ooguri: Was that the rst time eld theory true in supersymmetric of a new paper by Michael Dine and the spurion technique was used in theories? on gauge mediation of supersymmetric theory? The modern point of view, based supersymmetry breaking. (Later they Seiberg: Spurions had appeared on holomorphy of the superpotential collaborated also with Shirman and earlier, especially in the context of vindicated Gell-Mann’s principle and is with Nir.) They decided to take up the supersymmetry breaking. I think the consistent with ’t Hooft’s naturalness. same question about supersymmetry new point here was to view all the The superpotential is subject to the breaking that Michael, Ian, and I had ordinary supersymmetric coupling same genericity properties as every dropped when string theory came constants as spurions by viewing other term, except that when we use along. them as background super elds. And this genericity we should also take Ooguri: So, this was a continuation of the main application was to derive its holomorphy into account. For this your work with Afeck and Dine. Was the non-renormalization theorem. reason, I picked the title of my paper it roughly 10 years after that? Ooguri: Were you the one who “Naturalness versus supersymmetric Seiberg: Indeed. They did their work introduced this technique in non-renormalization theorems.” in 1992-1993. supersymmetric theory? For me that was very satisfying. Ann visited Rutgers and we talked Seiberg: I am not sure about that. Many different computations and a lot. At that time, I was tired of But perhaps that was the rst time many different phenomena were supersymmetry and I didn’t want all the coupling constants were understood together using one to go back to that topic. But she viewed as background elds in the organizing principle. I felt like I had succeeded to push me back into it... context of a supersymmetric theory. been circling around this for years and Tachikawa: You didn’t want to go I remember that within hours or so all of a sudden it all came together. It back? That’s surprising. after I thought of it many things fell was clear that that was the right way Round Seiberg: I did not want to go back into place. to think about it. Table because I thought“ Okay, I’ve I’d like to offer a historical Ooguri: When did you come to already worked on this, I want to do perspective. Before the 1980s there appreciate the importance of something new.” was a clear understanding that the holomorphy? Ann visited us at Rutgers and gave behavior of quantum eld theory Seiberg: The appreciation of the talks about her work with Michael satis es some genericity requirement. power of holomorphy of the

19 superpotential occurred to me But this was a separate line of should be able to address all the open gradually during these years. We development. It is surprising and questions in quantum eld theory have seen many examples of interesting that similar ideas came up using holomorphy.” computations of a superpotential, independently in different contexts at As a rst step I looked back at the where the real part and the more or less the same time. supersymmetric version of Quantum imaginary part were computed As we discuss historical Chromo Dynamics. With Ian and independently, and surprisingly the developments in science I am Michael, we had understood the result turned out to be holomorphic. reminded of the famous Kurosawa behavior of the theory for small At the time this looked like a miracle movie Rashomon. number of avors, so I wanted to and a non-trivial consistency check Tachikawa: It is based on a book understand what happens with of the computation. by Akutagawa that we studied in more avors. Armed with the new Using this for a non-renormalization school... perspective and new tools I realized theorem was also not completely new. Seiberg: I am not familiar with the that although the vacuum degeneracy For example, Edward Witten argued book, but I really like the movie. of the classical theory is not removed for a perturbative non-renormalization One lesson from that story is that in the quantum theory, extremely theorem in the string worldsheet different people view the same interesting effects are still present. using holomorphy and Michael Dine reality differently. This is common For example, the complex structure and I used similar reasoning about in the history of science. There are of the moduli space of vacua can be string perturbation theory. In those several lines of development and they deformed in the quantum theory. In cases, the holomorphic dependence are typically motivated by different other cases, there are new massless was on elds, not parameters questions. So if you interview composite particles. That was (although these were parameters in another researcher who worked surprising. Until then it had been the worldsheet theory). Holomorphic at the same time, you are likely to believed that with strong dynamics dependence on parameters in hear a completely different version the theory is gapped or has some 3+1 dimensional eld theory also of the events. And it is not that one massless Nambu-Goldstone bosons. appeared in papers of Victor Novikov, description is more correct than Here, on the other hand, there can , Arkady Vainshtein, another. They simply reect different be massless composites that are and Valentin Zakharov and in an perspectives. not associated with spontaneous unpublished work that Joe Polchinski Going back to your question, at the symmetry breaking. Later, this and I did. And I must be forgetting time I was mostly interested in four- observation strongly motivated the other examples. dimensional quantum eld theory. understanding of the long distance Ooguri: That was in the summer of The idea that you could say anything behavior of N=2 theories (where 1993. But, in the late 1980s, you were about the non-perturbative behavior there are massless monopoles) and essentially using it, weren’t you? of four-dimensional quantum eld other N=1 theories (where there are Seiberg: Indeed, I use it. But at the theory was totally unimaginable. massless composite gauge elds, time I did not view it as the underlying Ooguri: Right. You would not have massless glueballs, massless exotics, organizing principle. expected that there would be analytic etc.). Ooguri: That’s interesting because control over any non-perturbative Then I started working with Ken that was also the year I wrote this physics in four dimensions. Intriligator and Robert Leigh on paper with Bershadsky, Ceccotti, and Seiberg: With the understanding of increasingly more complicated models Vafa on topological string theory, holomorphy as an organizing tool all and we saw that the new techniques which also used the holomorphy of a sudden things became clear and are very powerful leading to many and its relation to supersymmetry to easy. new exact results. derive the recursion relation, the so- Ooguri: So, that became the guiding Then wrote an called BCOV equation. principle. extremely interesting paper… Seiberg: Your paper was a milestone. Seiberg: When you have a new tool Ooguri: Are you talking about his It clari ed many issues and it led you should be maximally ambitious. work on monopoles? to many signi cant consequences. I remember that I thought“, We

20 Kavli IPMU News No. 34 June 2016 Duality and Seiberg-Witten everyone thought that this should not a special case of N=1. The speci c Solutions be used as evidence for duality. properties of N=2 are nice and allow Seiberg: Yes. I am referring to Sen’s In addition, duality demanded the you to compute additional quantities. paper establishing the existence existence of a certain bound state of But for the question of con nement of a charge-2 monopole in N=4 two monopoles in N=4 theories. And they are not essential. supersymmetric theories. That it was thought that such a state does If you go back some time – I think paper removed a real obstruction to not exist... it was in the fall of 1987 – Witten duality. People had thought about Ooguri: Yes, but then, Ashoke’s wrote a paper explaining Donaldson duality before that paper. I think demonstration of the bound-state theory as a twisted version N=2 it was Witten who emphasized was... supersymmetric Yang-Mills theory. It the importance of this charge-2 Seiberg: …a phase transition. Before made Donaldson theory accessible monopole. And it was believed that that paper duality was viewed as to physicists. But it didn’t solve that such a monopole does not exist and some technicality. Some things look as mathematical problem. therefore the whole idea of duality if they’re dual, but there is no reason Ooguri: It gave a physical had to be wrong. Sen’s paper found to believe this duality was an exact interpretation of the mathematical that monopole and overnight it was statement. Then, overnight it became problem. clear that duality must be right. obvious that duality is crucial. Seiberg: But I am told by Ooguri: Since Yuji is here, maybe one Ooguri: Did it convince you that mathematicians that from their of us should explain it to him. In early duality is actually a real phenomenon viewpoint it didn’t solve the problem, 1990, not too many people believed in quantum physics? because at the end of the day you had in the electric-magnetic duality, the Seiberg: I was immediately convinced to do exactly the same computations S-duality. that it was true in N=4 theories. But I that Donaldson did anyway. Tachikawa: Yes, I came too late to this did not imagine that it will play such However, viewed more broadly, part of the party. a crucial and central role as it later this is an amazing paper. In this paper Ooguri: There was of course the work turned out to do. Edward Witten introduced the notion by, I think, Montonen and Olive and And then I started collaborating of a Topological Quantum Field then Olive and Witten, and… with Edward Witten on the N=2 Theory. This is an extremely deep idea Tachikawa: Goddard, Nuyts and supersymmetric theory. with far reaching consequences both Olive? Ooguri: Were you interested in in mathematics and in physics. Ooguri: Right. But, when I read the N=2 theory before you started When I heard about that work Olive-Witten paper in the late 1980s, collaborating with Witten? I used my tool-kit of instanton I had an impression that rather than Seiberg: Yes. I viewed it simply technology to write a short note giving evidence for duality, they as another theory with N=1 on the N=2 theory thinking about were actually explaining why this supersymmetry. And as I was working its moduli space of vacua and miraculous formula works without out examples of increasing complexity showing how the metric is corrected duality – everything comes from with N=1 supersymmetry, this was a asymptotically. I didn’t even want supersymmetry. natural member of that list. Also, it to publish that paper because I did Now we use it to motivate duality. was clear that the pure gauge N=2 not think it was interesting. Edward But at that time, it was basically theory has massless photons and the encouraged me to publish it. In fact, explaining that you don't need duality. pure gauge N=1 theory was expected in his paper on Donaldson theory, Seiberg: They considered states to con ne. So I was hoping that a he said that the ideas in that paper in small representations of the better understanding could explain may well be important for further Round supersymmetry algebra. Today we the mechanism for con nement. developments of the theory. He was Table refer to such states as BPS states. And Ooguri: And, you did. Did you think completely right about that. That was they explained many of the special that you had a better chance of doing in 1988. properties of these states as following that in the N=2 case, as opposed to Ooguri: That turned out to be the from this fact. Since these special N=1? starting point and the boundary properties had a rational explanation, Seiberg: I was viewing it more as condition of what is now called the

21 Seiberg-Witten solution. N=4 and N=2 theories, and they Ooguri: You told me that you heard Seiberg: Yes. I wrote the paper on exhibit similar dualities. Second, here about the Seiberg-Witten theory the“ Behavior at In nity” but I didn’t one nds weakly coupled composite by reading a popular mathematics pursue it. Then, in 1994 when I came gauge elds. This underscores the magazine. back to supersymmetric theories, I fact that gauge symmetries are not Tachikawa: Yes, there was an remembered my 1988 paper. I knew fundamental. This point had been interview of Edward Witten by Tohru that the vacuum degeneracy was known before, mostly in the context Eguchi in Kyoto. That was I think, early not lifted and an in nite series of of Abelian gauge theories, but here it 1994. instantons corrected the metric on the was more dramatic. Ooguri: That’s correct. Witten came moduli space of vacua. The question In the meantime, Witten wrote to give a public lecture in Kyoto was how to evaluate it and how to the paper on the connection of our sponsored by a Japanese company, sum up the series. solution of N=2 supersymmetric and I was involved in coordinating As I said, at the time Ken Intriligator, gauge theories to four-dimensional that. Rob Leigh, and I were collaborating. topology. Tachikawa: Edward told Tohru that he We wrote a paper studying various Ooguri: Yes, which is now called the was extremely excited about the work models in which the superpotential is Seiberg-Witten equation. It turned he was doing with you – without given by an in nite sum of instantons. out to be more powerful than the explaining much. But that was We succeeded to sum up the in nite original Donaldson theory. published in this popular Japanese series in an explicit closed-form Seiberg: Physically, it is very clear magazine in the summer of ’94… formula using the knowledge of the because many of the complications Ooguri: Before the paper appeared. It singularities of the superpotential and of Donaldson theory were associated was the rst printed announcement its asymptotic behavior, combined with small instantons. And every time of the result. with its holomorphy. So I was you have a computation associated Tachikawa: Then, Japanese optimistic that the same thing could with a new manifold you have to mathematicians like Fukaya got be done also in the N=2 theory. control the same small instantons. very interested in Seiberg-Witten When I started collaborating What the renormalization group theory. And Fukaya started to write a with Witten progress came in a allows you to do is to compute the series of introductory articles about stunning rate. Within weeks we had small instantons once and for all in at the Seiberg-Witten theory from the complete solution of the pure space and to nd an effective theory mathematics point of view in that and the theory with without them. Then you can place popular mathematics magazine. So matter. All sorts of interesting physical that effective theory on the curved for the rst few years, I thought of phenomena were elucidated including space of interest. Since this effective the Seiberg-Witten theory as a purely con nement and chiral symmetry theory no longer has these small mathematical thing. breaking. instantons, many of the complications I only learned about the physical Witten immediately realized that it in the original theory are no longer part of the Seiberg-Witten theory would help simplifying the problem present. So that’s the reason it was... after I started learning supersymmetric with four-dimensional topology. But, I Ooguri: In the effective theory it’s theory and nally I came across the was more interested in understanding already built-in, so you don’t... review article by Peskin. the dynamics of four-dimensional Seiberg: It’s already built-in and you Seiberg: The TASI Lecture? quantum eld theory. don’t need to worry about that. In Tachikawa: Yes, TASI Lecture. And Immediately afterwards, I wrote fact, the low-energy theory doesn’t then I nally understood what Seiberg the paper on duality in N=1. In that have small instantons. So that’s what duality was, from the physics point of paper a dual description of N=1 made these equations so much more view. That was already 2003 or 2004. supersymmetric gauge theories was powerful. That’s a long time to come. presented. This work taught us many Ooguri: [Looking over to Tachikawa] lessons. First, it was realized that Were you in high school in 1995? Second Superstring Revolution electric-magnetic duality is ubiquitous. Tachikawa: Yes. Well, that’s about in 2005 N=1 theories are more generic than when I rst heard your name. Ooguri: When did you hear about

22 Kavli IPMU News No. 34 June 2016 Witten’s breakthrough in string duality? Seiberg: He told me bits and pieces of it as he was working. And then I heard the nal version when he gave the talk at USC. Ooguri: At the Strings 1995 Conference. Seiberg: I was on sabbatical at the Institute at that time. We spoke the week before the conference and he told me that some of these things would actually work. But it was still very, very different from what he presented at the talks. I was stunned in the talk. I was supposed to give the talk after him and I felt“, What am I space of vacua, degrees of freedom at student, I studied Coleman’s lecture doing here?” strong coupling, etc. notes, where he described – I quote, Tachikawa: What did you talk about? But there were also other lines “the glorious victory parade, full of Seiberg: I talked about eld theory of development. The work on wonderful things brought back from duality, which was a few months old 11-dimensional of far places to make the spectator gasp and most people had not known Michael Duff, Christopher Hull, Paul with awe and laugh with joy.” These about it at that time, so I thought I Townsend, and others was crucial. discoveries happed in the 1970s, and I had a good talk to present. But after And the study of supergravity missed all... Witten presented his picture of string solutions of various solitons and Seiberg: And in the 1970s, they talked duality it seemed that my talk was extended objects by Gary Horowitz, about the glorious parade of ideas in already obsolete. and others was the 1930s and 1920s. It is always like Ooguri: That was a stunning talk, I also essential. that. remember. So there were many different There is no sign that this sequence Seiberg: In his lecture he spelled out developments that came together and of exciting discoveries will slow down. almost the entire picture. the string duality picture put them And based on past experience, I I got on the stage and being very all in a coherent picture. I think they expect that this will happen again and embarrassed I said“, I feel like I should enhanced each other because some again. And, as always, I expect it to drive a truck.” Then I gave my talk. I aspects were clear from one point happen in surprising ways. don’t remember the rest of it, but I am of view and other aspects were clear There is always somebody working told that John Schwarz, who was the from another point of view. Together on a project that most people think is third speaker in the session, started they combined to a complete and totally uninteresting and unmotivated. his talk by saying“: If Nati has to drive coherent picture. Then that project turns out to be a a truck, I should drive a tricycle.” Ooguri: Yuji, which year did you go to real breakthrough. Ooguri: The eld really made a phase the Institute? For that, we just need to keep an transition in that year. Many of the Tachikawa: That was 2006. I only open mind and be accepting of other ideas that you developed in quantum joined this string theory community ideas. We should have this liberal Round eld theories, supersymmetric long after all of the things you were point of view. Let everybody do Table theories are now incorporated into it. discussing. Whenever I hear about the what they are doing and encourage Seiberg: Witten described the many glory days of 1984 or 1995, I always diversity. If everybody is working on developments leading to this point envy... the same problem, we will not have as spokes of a wheel. So this was one Ooguri: This will repeat itself. For these ideas from left eld that we spoke – supersymmetry, BPS, moduli example, when I was a graduate really need.

23 In addition, it is satisfying that these more question to ask. You have been Unity of Science phenomena appear in the real world very successful in running research Tachikawa: Can I jump 20 years from and are connected to real materials. groups and mentoring students and 1996 to 2016? Ooguri: You can test these ideas with postdocs. What do you think would Seiberg: Please. experiments. make successful research groups? Tachikawa: So you recently wrote a Seiberg: And it is likely that these new Seiberg: First, I should not get the paper on condensed matter physics, ideas will also lead to new insights credit for that. Whenever I was in a which you will talk about tomorrow. in quantum eld theory, which then research group I had many colleagues, What motivated you to get into this could be brought back to high-energy who made essential contributions subject? physics and string theory. to the scienti c atmosphere and to Seiberg: This is a fascinating topic. Many of the ideas in the study of running the group. The condensed matter physicists have topological phases of matter started Here at Kavli IPMU you clearly do made incredible discoveries. I would in high-energy physics. For example, the right thing. You have an excellent like to understand them. anomalies, Callan and Harvey’s vibrant group here. Some of the I’m a rm believer in the unity of inow, braiding statistics, world leaders are here at Kavli IPMU. science. I don’t like it when people Witten’s topological quantum eld These are people, whose papers I are put in boxes: one of them is a theory and others are the main tools always study carefully. In the last particle physics phenomenologist, that are being used. few days I have watched the group another one is a string theorist, and So I think there’s a potential function and I found it a real pleasure. another one is a condensed matter for high-energy theorists to do I have attended interesting talks and physicist. We are theoretical physicists something useful here. There are clear I have participated in stimulating and there are no clear boundaries indications that a lot more can still conversations. So all I can say is keep between the different sub-disciplines. be done. And I hope that I’ll be able doing what you are doing. Instead, over the years we have seen a to contribute. But at the very least, I’ll As a general advice, I would suggest lot of cross-fertilization from one eld learn something new and it is always to create a stimulating environment to another. refreshing to learn new things. by creating a diverse group of people. Hirosi and I have just returned from Ooguri: This time, non- There should be people of different a symposium in Chicago celebrating supersymmetric theories. seniority level, of different talents, of Yoichiro Nambu’s career. The Seiberg: I have worked in the past on different kinds of expertise, and of importance of interdisciplinary physics related topics like topological theory different backgrounds. For example, was very visible there. Nambu’s work in connection with rational conformal there should be mathematically is a perfect example of ideas from eld theory. So I think I have some oriented individuals, people with good one branch of physics imported into tools that could be helpful. physical intuition, good calculators, another branch of physics leading In general, there is no guarantee etc. to enormous impact and to useful that any research project or direction I would encourage everyone to cross-fertilization between elds. will be successful. I always tell my interact with each other and to talk This is clearly demonstrated by his students and postdocs“, Doing about their research. So that when a most famous paper with Giovanni research is a risky endeavor. There is question arises, there will always be Jona-Lasinio“, Dynamical model of no guarantee of success. You must try somebody who can nd the answer. elementary particles based on an many things hoping that one of them There is also a question of how to analogy with superconductivity.” succeeds. But you should be ready to select postdocs. I don’t think there’s a Going back to your question about accept that most of them will fail. We clear predictor for a postdoc success. my current work on the topological do that for the few successful days in Instead, I think we should not attempt phases of matter, I am simply trying which we learn something new.” to make the perfect selection, to learn these beautiful ideas. These because this is impossible. We should are fantastic phenomena that eld simply attempt to collect a diverse We Cannot Predict the Outcome theory exhibits, and I think that every group of researchers and to create for eld theorist must understand them. Ooguri: Before we nish, I have one them the right atmosphere.

24 Kavli IPMU News No. 34 June 2016 Another suggestion is to ask the that you followed your nose and postdocs what they think would help pursued things you were interested them. in, like techniques in supersymmetric Tachikawa: When I was at the theory, which later turned out to be Institute you suggested to me to very useful. have a meeting of the postdocs with Seiberg: I think I was lucky. I did not Pizza... have a long-term plan, maybe a year Seiberg: I think this was your idea. in advance but not more than that. Tachikawa: Was it mine? Anyway, Well, I think the same is true for your eventually we started a“ Pizza papers. There was no way you could Discussion” every week in the predict 2 or 3 years ago the topics afternoons. you are interested in today. Ooguri: No faculty? The reason research is interesting Seiberg: The faculty were not allowed. is because we’re surprised by the Tachikawa: Right. That was a lot of fun. answers. If we could predict the Can you offer some vision for the answers, we would not be surprised future? by them. Almost by de nition, we Seiberg: Some people think that cannot predict the outcome. So we researchers should have 5-year should not attempt to do that. programs – like in the old Soviet Pursue what you’re interested in, Union – where everything is planned keep working hard, pay attention in advance. Solve this problem and to what’s going on around you and then move to the next problem and be exible – these are the rules. then... Sometimes it works, sometimes it Tachikawa: We still have that system doesn’t. in Japan. Seiberg: That might make some sense for experimentalists. But theorists’ progress is more like a random walk. Theorists are stimulated by many sources. They listen to seminars, participate in informal discussions, read papers, etc. This impacts their research direction in unexpected ways. It might even lead them to abandon their existing line of research and to start another one. And even within a given project, in most cases the outcome of the research could not be anticipated from the beginning. In our conversation about my research path I shared with you some Round examples of such unexpected results Table from my own experience. So there is no way I could outline what I’ll be doing in the next ve years – this is ridiculous. Ooguri: Well, your example shows

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