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With Gerard T Hooft

With Gerard T Hooft

Interview with Gerard ’t Hooft Interviewer: Shigeki Sugimoto

Physics Had Been Primary than learning to read and Interest since Very Early write. In Europe, in general, Age when you’re 6 years old Sugimoto: Thank you very you learn how to read and much for letting me have write at least the basic stuff. this opportunity to talk to Before that, I could not read you today. There are a lot of or write but I could add and things that I wanted to ask subtract, and I knew that I you. was interested in that. ’t Hooft: Yes. Sugimoto: In mathematics? Sugimoto: First, I would like ’t Hooft: In mathematics and to ask you when and how you . Physics was running got interested in . in my family to some extent. ’t Hooft: I think that I was My uncle was a theoretical somewhat exceptional. . He was well known When I was still very young, in his eld. My grand uncle maybe even at nursery was , who also school, I really knew that I had a in physics. was going to be interested I was very much inspired by in the world of nature. I that and from an early age had much more dif culty in on I knew I was interested in understanding humans than physics. nature. I also found adding Sugimoto: I see. When did and subtracting much easier you decide to be a physicist? ’t Hooft: Well, I don’t know when I really decided to be a Gerard ’t Hooft is Distinguished physical scientist but physics University Professor at Utrecht University (since July 2011). He shared had been always my primary the 1999 interest. Maybe 9, 10, or 11 with Martinus J. G. Veltman“ for elucidating the quantum structure years old, I knew that I was of electroweak interactions.” He going to be a physicist. has also received many other distinguished awards including the Sugimoto: Then, you Dannie Heineman Prize in 1979, became a Ph.D. student of in 1981, Lorentz Medal in 1986, Franklin Medal in Veltman and soon after 1995, Oskar Klein Medal in 1999, that you started to work and Lomonosov Gold Medal in 2010. He received his Ph.D. from Utrecht on the renormalizability of University in 1972. In 1977, he Yang-Mills theories. Is that became a full professor at Utrecht University. right?

14 Kavli IPMU News No. 30 June 2015 Started to Work on the to replace it with something Renormalizability of better, something where you Yang-Mills Theories don’t have to renormalize ’t Hooft: Yes. Veltman was away in nities. There were working on the problem of many electroweak theories. how to renormalize Yang- One approach was called the Mills theories and he had scattering matrix approach, developed some very good, another was called current sound techniques which algebra; there were all sorts fascinated me. But he said, of algebraic ideas about how “This is very dif cult” and to understand elementary “It may be better for you to particles, but eld theory was work on something else.” not at all popular in those But my reaction was“, Well, I days. like the problem that you are Sugimoto: I see. What was working on very much. I want the reason that Veltman and to understand more of that.” you believed in ? From the beginning I said“ I ’t Hooft: Veltman was very understand your dif culty, so pragmatic. He understood I want to see what I can do there was a basic problem about it.” in understanding the weak Sugimoto: I heard that many interactions. He learned people were skeptical about about the experimental gauge theory at that time. observations. Experimentally, ’t Hooft: At that time, yes. a lot was already known It is a bit dif cult to say about the weak interactions how the history developed and about other properties of because now people are very particles and forces. Also, their much tempted to say that symmetry structure was very there was such a thing as well understood since Gell- the electroweak theory and Mann’s theory became the only question was how a well-known topic. It was to renormalize it. But that is understood how important Interview not how they looked at their problems at that time. I mean Shigeki Sugimoto is Professor at the majority of did the Yukawa Institute for Theoretical not want to think in terms Physics, Kyoto University. He is also Visiting Senior Scientist at the Kavli of eld theory. They wanted IPMU.

15 group theory, Lie groups in to do it. completed the proof of Found the Way to Cancel particular, is for physics. That Sugimoto: I see. renormalizability? All the Anomalies was clear but how to get the ’t Hooft: He had all the ’t Hooft: I rst thought, ’t Hooft: I realized,“ Well, exact description of these ingredients but there was “I will need to convince now I understand exactly particles was a big mystery. still no answer about how people that this is the way how to do it and I have Now, Veltman even did not to renormalize this theory to do things,” because there to ll in some details,” care pretty much about properly. At that time this was was a sentiment against but those were secondary eld theory although he thought as just one possible . So I realized details. The most important liked the general formalism, approach to physics and it that people were going to detail was the anomalies. It but he just repeated what was not expected that this criticize whatever I had done wasn’t obvious that if you everybody else said that eld was going to be the way to and Veltman had the same renormalize this diagram theory is probably not going understand all the forces in response as well“. Maybe you using this counter term, to be the answer. But in the nature. have something interesting and that diagram using that meantime there was nothing Sugimoto: Were there many here, but people will ask this counter term, if you combine better to do. He thought people trying to prove the and that. Do you have your the whole thing it will still that eld theory might not renormalizability at that answers ready?” I realized be unitary; and indeed a be the answer. But it was time? that people were going to ask counterexample was known. the thing I understood that I ’t Hooft: No, there were not quite a lot of questions which There were examples of could do in principle, except so many people who were I could not answer. This is a theories where this would we did not understand the studying renormalizability. very mathematical problem. break down; that was the details. We basically did not There was , Mathematicians are very case when you have chiral understand how to handle there was , accurate and I was somewhat symmetry; left and right the renormalization effect of but they were asking more sloppy in the way of phrasing particles are different. particles with the exception of generic questions like“ How things. He said“, This is where Sugimoto: The chiral the . The photon was in the world can these things you have to be more precise. . understood; actually the best- hang together?”“ How do we Otherwise nobody will believe ’t Hooft: The chiral fermion understood particle. describe these forces?”“ How you.” has anomalies in it. Those Sugimoto: Right. can we understand what the Sugimoto: Were you excited anomalies would be ’t Hooft: That was a vector next particle will be that is about this? disastrous. Now not every particle, so why was it so going to be discovered?” and ’t Hooft: Yes I was very theory has such anomalies, at dif cult to renormalize other so on. But, renormalization excited because this was least not that we knew. But vector particles? The problem was not very fashionable. certainly the moment when still there was this danger; was in the masses of these Sugimoto: Did you think I realized the importance of maybe there are more such particles. Veltman understood you would succeed when you the . I didn’t anomalies. While formulating that the weak interactions started tackling this problem? really call it that because I the rules to renormalize the are caused by vector particles ’t Hooft: Well, as long as I didn’t know the papers by theory, we have to prove that with mass, and he tried to hadn't been able to answer Higgs and Englert very well. everything hangs together understand how to make the main questions I didn’t I had heard that there were without any anomalies a unitary renormalizable know whether I would people thinking along these because if they were there, theory for such particles. He succeed or not, but I was lines. So I accepted that I was we could understand that had discovered many of the very ambitious and I knew not the rst to write down renormalization would problems that were there. He for sure I wanted to get the these theories, but I did feel destroy unitarity, which had his own approaches to best answers I could nd. So I I was the rst to understand would imply that it would the problems using gauge thought“ If this problem can how exactly the Higgs not really work. invariance and he was be solved at all I will try to mechanism was solving the Sugimoto: Right. intrigued very much by the solve it.” problem that Veltman had ’t Hooft: I had some hopes Yang-Mills paper. He said this Sugimoto: I see, so how formulated. that if there are anomalies, should be somehow the way did you feel when you Sugimoto: I see. maybe you can nd a way

16 Kavli IPMU News No. 30 June 2015 to rephrase the theory such In itself that nearly worked Story of the scaling, but I never quite that it still is unitary, but that but it just didn’t and then of Yang-Mills Theory understood what Bjorken hope quickly evaporated. I discovered the correct Sugimoto: I heard that you meant when he talked about No, you have to cancel out answer or a much better also knew that the beta scaling. People said“, Bjorken all the anomalies but how answer by taking four plus function of Yang-Mills theory scaling proves that eld restrictive is that? Will there or minus epsilon dimensions is negative before the work of theories don’t work.” I could be any theory where all the and letting epsilon tend to Gross, Wilczek, and Politzer. not understand why they said anomalies cancel out? This zero. That was the correct ’t Hooft: Yes, that is a that because I thought“, Well was not known. answer. It was amazingly so somewhat strange story. Of when I scale the theory, it just Sugimoto: I see. At that time, because you can ask“ What course I was approaching the works ne. I don’t understand the cancellation of does it mean, four plus or problem from the physical your problem.” But what I the was not minus epsilon dimensions?” point of view. As a physicist, did not realize is that nobody known? Physically it makes no sense, I wanted to understand how had yet calculated that beta ’t Hooft: No. Well, it was and mathematically it makes these elds work in practice. function. known that fermionic no sense. But I noticed And then, it’s very important Sugimoto: Why didn’t you anomalies may be made to where epsilon comes in the to know how this system publish this? cancel. This was not certain, expressions it is just a number works at very short distances ’t Hooft: First of all, I thought but I thought maybe the in a diagram which you and how it works at very there was a more urgent pure gauge part itself also can tune any way you like. large distances. Very early, problem. The urgent problem has anomalies which we do You can choose a complex well before the dimensional was to understand why not know how to cancel. It number if you want, and you renormalization and such, I are con ned because had to be proven that they can choose to let it go to zero. asked myself what happens in this would be a theory for cancel. The point is that the Sugimoto: How long did the short-distance limit. the strong interactions. The number of counter terms it take for you to prove this Sugimoto: Before real problem of the strong that can be used was not renormalizability? dimensional renormalization? interactions was the quarks. as large as the number of ’t Hooft: One of the ’t Hooft: Yes, because if the Why did they not come out free parameters one has to questions is, how long did short-distance limit theory is as free particles? I thought renormalize. So, I realized it take to convince myself? suf ciently convergent, then we now had one half of there could be a clash, so That was fairly quick, a all I need to do is to establish the answer to this question, that even though the theory year or so. Certainly after things at one or at most two but the other half is what looked renormalizable, things dimensional renormalization loop levels. Everything else happens in the in nite could go wrong if you try to was introduced, I realized this will become unimportant distance region and that was work out all the details of all is the answer and I don’t need because if the theory is totally much more dif cult, of course. the diagrams; you will nd any further proof but that is free that’s all you need to I think Veltman put me a little that they are contradicting not exactly the same thing know. So I did the calculation, bit on the wrong track here each other and then the as a mathematical proof. To I scaled, I had the nal in that he said“, Well as long theory will not be unitary. So prove that it works correctly diagrams, and I could see how as you don’t understand why this was still something that to all orders: that was the they scaled. I thought“, Well these quarks don’t come out, had to be proven. What was main thing really. The way this is just ne.” It has the you have nothing ̶ it is not missing was a good way to we phrase the problem is: right sign to be what are now even worth publishing.” That regularize the theory and that prove that all nal diagrams called asymptotically free. I was a mistake. Of course, I was where basically I had the up to any number of loops could clearly see that the sign should have. Yes, I believed idea of varying the number of can be renormalized using implied what is now known in the theory but I hadn’t Interview dimensions. dimensional renormalization. as . So understood that I was the I rst tried ve dimensions, That required some extra I couldn’t understand why only one who had calculated six dimensions, seven work but it was quickly sorted many people had such beta function correctly, and dimensions, and used these out that this indeed was the problems with it. There was understood that it is negative dimensions as regulators. best way to do it. an argument about Bjorken and so the pure gauge theory

17 would serve very, very well particles, but they behave as a and can we mathematically Sugimoto: Do you think it as a candidate for the strong single coming out with even de ne what a mass will be proven someday? interactions. Now we all high energy. Those quarks gap is? The question is if ’t Hooft: I think it will be. I know how this leads to the will then manifest themselves you know how to de ne the think what we need is some con nement of quarks, but as jets and the also theory and know how to monk on an uninhabited that was just a big conjecture as jets. So you have quark de ne the question, can we island who sits in a monastery in those days. jets and jets. And that prove this property of the with his books and his Sugimoto: I see. Was it easy was how unitarity could be theory? computers and his laptop for you to accept QCD despite understood to be restored; The strange thing is that the and his internet and he just the fact that quarks and but those items were quite best procedure we have today works out the proof. There gluons were not discovered? complex. They need not is that we prove it numerically. are hundreds of epsilons and ’t Hooft: Oh, yes because just hand waving but some We simulate this theory on a deltas that you have to put I thought there’s absolutely more rigorous mathematical big computer by putting the in the right position and then no reason for these quarks treatment. thing on a lattice. We take I think you can prove it. I do to come out as free particles Sugimoto: Do you think the lattice as ne mazed as believe that this is a property because they have color con nement in QCD is possible and then we see that of our physical theory. We all and all physical states must understood well enough the theory behaves exactly believe it’s true and therefore be invariant under color. these days? as all physicists expect. So we all believe it can be proven, You can turn the question there is no problem. They say but it’s going to be a very around. Why should there be “We can prove everything tough and very unrewarding Con nement in QCD: free quarks? The answer is Acceptable as a Physicist, in mathematics; the rst work because after 20 years they are not there. I thought But Unsatisfactory as a 10 decimal places obey the monk would come out Mathematician basically I understand that the this theorem, so indeed all of his monastery and he says, theory doesn’t have to have ’t Hooft: I think the numbers obey this theorem.” “Look I have proven QCD free quarks. But, the question combination of these That doesn’t go with to exist,” and all physicists is then what keeps those items to me as a physicist mathematics. Mathematicians will stare at him and say quarks together? How do you is quite acceptable and it will not accept this as a proof. “What’s your problem? Why understand that such a theory explains everything. But as Of course not. They shouldn’t. have you been doing all this will be unitary if you don’t a mathematician, I would It’s still a problem in physics, work? We knew that QCD understand the physical states, say“, Well the situation is but I think it’s an academic is a ne theory.” So he will the asymptotic states of the not as good as it should problem. We don’t need not be rewarded. Probably theory? That was basically be.” QCD is not at the same that problem to be solved to he might not get the Nobel answered by several pieces of level of accuracy as quantum understand how QCD works, Prize for it even though it’s a insight. One was the fact that electrodynamics and the but we do understand that very important mathematical there are vortices and that the con nement problem is part it needs to be solved from question. mechanism that keeps them of that. It’s now called the a mathematical point of stable was a dual opposite problem. That is, view. The importance of a 1/N Expansion and String of monopole con nement, “Does a pure gauge theory, mathematical proof may well Theory called the Meissner effect QCD, generate a mass gap?” be that if you have proved this Sugimoto: I see. Another in superconductors. It’s the The question immediately mathematically you also might thing that I wanted to ask you dual Meissner effect, and associated with that is“, Can nd new alleys to do faster is about 1/N expansion. How the realization came slowly we compute the mass gap?” and more precise calculations. did you come to the idea of that you can understand “Can we understand what the It won’t be a waste of time expanding amplitudes with everything with that. lightest particles are in QCD?” to prove mathematically that respect to 1/N? The other thing was jet The answer is that are the mass gap exists because ’t Hooft: At that time I was physics: that the asymptotic basically the lightest particles then you can actually make at CERN as a fellow and all states are not free quarks but of QCD, but can we prove this accurate computations for these marvelous new ideas jets. Jets consist of hadronic with mathematical accuracy everything. came along, and one question

18 Kavli IPMU News No. 30 June 2015 was exactly the question which I mentioned“, How to have good approximation techniques for QCD?” Is there a small parameter in QCD? Is there a parameter you can tune even if physically it might not be so small such that, if you tune it to be very small, calculations can be done accurately? If the parameter will be larger, the theory is slightly less accurate but certainly you have a systematic expansion. Of all parameters, of course, 1/N came along as a parameter and I asked myself now“, In what way does the large-N theory distinguish itself from arbitrary N theories? survived and they looked very N to in nity limit of QCD. interesting mathematical What does the limit N to much like the world sheet Maybe that’s a theory that approach to quantum in nity look like?” I knew diagrams of a . can be written down in a , but not suf cient. I that a certain simpli cation By that time we understood closed form. The point is that think physically there’s got took place in the diagrams. I that there will be vortices that the 1/N to zero limit, or the to be more. You have to wanted to understand“ What connect the quarks together. N to in nity limit, is a limit make a distinction between kind of simpli cation is that?” So this will be a perfect where the and the the physical question and I found the answer to that. way to understand where do not interact. It the mathematical question. Unfortunately, the answer was these vortices come from, in is a free theory and for that Mathematically, string that even in the N to in nity principle. reason, you might suspect it theory is a very interesting limit, the nal diagrams Sugimoto: So, this 1/N is exactly solvable. Free theory mathematical construction. It can still be so complex that expansion resembles the is basically trivial. All you need should be taken very seriously you cannot compute them perturbative expansion of to know is the mass spectrum. in trying to understand exactly. We cannot do the string theory. I thought string theory should , but large N expansion explicitly. ’t Hooft: Yes. help me do this. Maybe the physically I think the ultimate The power expansion in that Sugimoto: Did you think that 1/N expansion is equivalent underlying equations are not expansion constant generates it can be used to formulate to a string theory. I hoped to string theory. But I am in a all the planar diagrams. They string theory? see that happen. But though minority here. are too complicated to solve. ’t Hooft: That was certainly I tried many times, I couldn’t Sugimoto: You are the one I searched very hard to see if our hope, yes. I was hoping identify any string theory that who rst proposed the idea there is any way to get some that this would also vindicate coincides with the 1/N limit of of out of the sort of internal equation to string theory. It would tell you QCD. consideration of solve the large N diagrams for why all the dual resonance Sugimoto: Do you think entropy. Later Maldacena and Interview QCD, but that, up to this day, models were so successful string theory is a promising others re ned this idea in didn’t work. for the strong interactions. I candidate for quantum gravity the context of string theory. Of course, the question was wanted, in fact, string theory or…? How do you think about this extremely interesting because to solve my problem, which ’t Hooft: Personally I think development? only the planar diagrams is, I want to understand the that it is a very good and

19 It basically corresponds to the entire system, in principle. gauge theories, of dimensional How to Understand Physical Degree of what ts on the surface. Now That means the inside is also renormalization, and the Freedom of Quantum the physical implementation, understood. role played by the Higgs Gravity at Planck Scale I think, is different from what That is of course a very mechanism in renormalization. ’t Hooft: They really took you usually hear when people strange situation, and that tells The magnetic monopole was off in a direction which was talk about string theory and you quantum gravity is going a very fortunate moment, and never my intention. They are holography and AdS/CFT and to be a very crazy theory, so was the 1/N expansion, but using duality which is not so on. I think the physical unless you do it my way. My also there are some very nice quite the same as holography. reason is in the fundamental way is that you have to re- ideas about instantons and I nd dualities interesting origin of quantum evaluate our understanding their role in explicit symmetry but they are not going to be itself; holography tells you of itself. breaking of a theory. The an answer to our physical that the degrees of freedom And, if you replace quantum standard model doesn’t questions. They are going to t on a surface and not in a mechanics by a deterministic conserve number even be helpful. They are going volume in a bulk of space- theory, then I can understand though it looks – if you look to relate one problem to time. There must be a good the holographic principle at Lagrangian – that baryon another problem. Holography reason for this. The reason I much better. Then, it number must be conserved; is being used in the sense can nd is called information tells me that actually the but when you take the that certain different theories loss. The point is that all underlying quantum theory instanton effects into account, are equivalent. But that really information about a certain is not keeping all the baryon number is not never was my problem. The physical object in a volume inside information intact. conserved. That’s a very deep problem is how to understand of space is already to be Information dissipates away. and beautiful observation that the physical degrees of found on its surface. You can Imagine a surface, and we made. Those are essential freedom of quantum gravity, think of taking a region of the information that has things, and so I think they are and, in particular, at the space and time. The region dissipated away through the the best. Planck Scale. I am convinced is bounded by a surface. surface. Then if you know the But also, in a different way, that at the Planck Scale we If you look at all physical data on the surface, you have I am proud of what I did later only have bits and bytes of phenomena on that surface, all the information you need on in gravity and . We don’t have a you can actually reconstruct to be able to predict how the mechanics, although there continuum anymore in which what happens inside. If you inside of the thing will evolve are many that have to be things live. String theory is still think a little bit you nd that in time. That’s counterintuitive, proven. I would love to talk suggesting that you have to is not as strange as it sounds, but I have all sorts of ideas about gravity and quantum think in terms of real numbers because the gravitational now about how this can come mechanics with anybody and continua, and I have eld obeys Gauss's law, about in the ultimate theory but I didn’t have such great reached a stage now that I which really means that if of quantum mechanics. ideas there that solve the don’t believe anymore that you know the gravitational problem. I still see quantum the real numbers are going to eld on a surface, then you gravity as a big problem The Best Theory be the fundamental variables know exactly the amount of Is a Theory That that we don’t understand. I of all the ultimate theory. energy which is encapsulated Explains Experimental want to make fundamental Observations I think the ultimate theory by the surface. If you know progress there. Of course, we would just be based on bits the amount of energy, you Sugimoto: You have done so have to realize physics is an and bytes basically. But to have the Hamiltonian. In many ingenious works. Which experimental science in the understand how it works is other words, strictly speaking one of your works do you like very end. The best theory you now the big problem. We Gauss's theorem for gravity the best? can think of is a theory that don’t understand that. will tell you that if you ’t Hooft: Well, I think I proves or explains something Now holography tells you know the gravitational eld am still very proud of what that is being observed that the number of degrees accurately on the surface, happened in the rst few experimentally. What I would of freedom is actually even whatever that surface is, you years of my career that I had love to see is an explanation less than what ts in the bulk. have got the Hamiltonian of the idea of renormalization of as to why physical constants

20 Kavli IPMU News No. 30 June 2015 have the values they have, of asking d if cult questions, why the proton mass then maybe you will nd ratio has the value it has, some interesting answers. or anything of that sort, to You have to be extremely understand where constants critical. That’s the other of nature come from. That advice. In particular you have hasn’t happened yet. That’s to be critical about your own why I think that there is much results. You shouldn’t be more work to be done. happy with what you have found or what you have Advice to Young People understood so far. You should Who Want to Be always ask more detailed Scientists questions“, Did I understand Sugimoto: I see. Could you this?”“ Did I understand give some advice to young that?” and“ Why shouldn’t people who want to be the answer be formulated in a scientists? different way?” If you ask very ’t Hooft: Science is still critical questions to yourself, extremely interesting as an maybe you will nd some activity. When you are a new interesting answers. scientist you will discover Sugimoto: Okay, it’s about things, but usually you time. I really enjoyed talking discover very small things. If with you. you are hitting something ’t Hooft: Thank you. big that’s of course even a Sugimoto: Thank you very nicer experience. But you much. should realize that when you do some research on some topic, you want to know how that research relates to the ultimate questions that we are really interested in, like solving quantum gravity, nding the , understanding this and that. We won’t answer those questions overnight and the young students we see today may not nd answers to such questions overnight. But they might contribute some further steps towards nding answers. You can only Interview contribute if you understand what those big questions are. I think you should work on the big questions and if you are lucky and you are not afraid

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