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Credit: Jan-Olov Yxell, Chalmers University of Technology
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Interview of Lars Brink by David Zierler on May 27, 2021,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
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Interview with Lars Brink, Professor Emeritus in theoretical physics at Chalmers University of Technology in Sweden, with affiliations at CERN and the Max Planck Institute as well. Brink provides a broad historical perspective on the current state of play in string theory, and he conveys optimism that string theory remains the best path to developing a theory of quantum gravity. He recounts his childhood in Sweden and the interests that led to his undergraduate education in engineering physics at Chalmers. Brink explains his decision to remain at Chalmers for graduate work to study theoretical particle physics under the direction of Jan Nilsson, and he describes his interactions with Veneziano, Nambu, and Holger Bech Nielsen in Erice. He discusses the work of David Olive and John Schwarz during his time at CERN and his own focus on scattering amplitudes. Brink recounts the opportunities that led to his professorship at Chalmers, and he discusses the early days of supersymmetry at Nordita in Copenhagen. He describes his work on super conformal algebras, and his visiting professorship at Caltech where he worked with John Schwarz and Joël Scherk. Brink discusses the superstring revolution of 1984 and the optimism in finding a breakthrough to understanding gravity. He conveys his longtime interest in N=4 Yang-Mills theory, and he ponders whether supersymmetry would have been detected at the SSC. Brink discusses his work on the Nobel Prize committee, and he describes his feelings when the Higgs was discovered. He explains why supergravity remains a rich field and why he remains optimistic about new physics beyond the Standard Model. At the end of the interview, he predicts that one hundred years from now, fundamental physics will have advanced to a point of unifying simplicity.
Okay. This is David Zierler, Oral Historian for the American Institute of Physics. It is May 27th, 2021. I'm delighted to be here with Dr. Lars Brink. Lars, it's great to see you. Thank you for joining me today.
Thank you for calling me.
Lars, to start, would you please tell me your current title and institutional affiliation?
Well, I'm a Professor Emeritus in theoretical physics at Chalmers University of Technology. I also have an honorary position with the Albert-Einstein-Institute in Potsdam in Germany. I'm a foreign member of it, from which you don't retire. It's an institute in the Max Planck Society. So, this has been a place where I've been going to for longer or shorter periods. So, that's an extra bonus. Two and a half years ago I was also a visiting professor in Singapore, in an institute for advanced studies. It was called Institute of Advanced Studies, and I spent three months a year there for some five years. But then there was a new president and essentially, he threw us all out, which was sad because we had some marvelous conferences there. But also, I have a contact with CERN for the moment. I was supposed to go to CERN in August, and it will not work out. So, even though I'm retired, I'm pretty busy.
Lars, just as a snapshot in time, what's most compelling to you in theoretical physics these days? What have you been working on, and what are you following?
Well, you know, I've essentially been involved in string theory from the beginning. Of course, I'm always following it, and I'm one of the few that's never left it. On the other hand, I shouldn't say that I understand too much of what's really happening now. In the last ten years or so, I've been looking more at gravity, trying to find symmetries in gravity, extra symmetries, and also in Yang-Mills theory. I have this idea that, for example, in Yang-Mills theory, and especially in N=4 Yang-Mills theory, which is my baby, there are some miracles happening which makes it sort of a starting point for quantum field theory. But there is also something extra in ordinary gravity. It's remarkable that it works pretty well quantum mechanically even though it should not be working so well. It's working better than what meets the eye, I would say.
So, I've been working on that, and I've also taken up an old, almost 50-year-old idea, which came when we were working back then with string theory. I was at CERN at the time. We were then really trying to find a string theory for the hadrons. Of course, that's how the string theory started. We wanted to shortcut the way by really trying to use the physical masses of the low-lying mesons and see if one can see string-like behavior. We did that, but more or less at the same time, QCD came, and that was more interesting for hadron physics. So, somehow, I left it at the time, and then we went over to use string theory as a theory for gravity and other attractions. But I've always been wanting to come back to it, and I have made some progress recently. Well, I'm understanding the problem a little bit better now, but sitting here at home, not having too many to discuss with, I've not been able to make more progress than what I did a year and a half ago when I was a visiting professor in Munich for the fall semester in 2019. That's when I was working on it, and I was very excited, but then the pandemic came, so it's still lying there.
So, this is what I'm doing in physics. I'm not doing too much these days, I would say. This life at home takes more time, you know. We are trying to get a lot of exercises by walking around. But such things I'm thinking about. And then I have also some commissions with Zoom meetings. This is where I am.
But you also asked me what I think about what's interesting now. That's a more difficult question because I think the string community, in a wider sense, is searching. You probably have found that from other people in my generation that we don't go as fast as we once did way back in the 1980s. On the other hand, I think most of us who were active then still believe this is the right way of attacking fundamental physics. It's just that it is more difficult. We are very far from sort of the commonsense physics that we usually base what we're doing on, even when we do quantum theory. So, it is really very difficult to work up an intuition for what is happening at the fundamental scales. What I really hope is that they will find something new at CERN. There are some indications at CERN and Fermilab which could be what we're waiting for. There are all sorts of promising experiments that should give us hints about dark matter, and other expected things. If that comes, I would really like to go back to more ordinary particle physics. I guess I'm probably too old for that, but that's where in a sense, my soul is, in particle physics.
Lars, on that point, in particle physics, you mentioned Fermilab. It's been fun asking eminent physicists what they think about the current g-2 muon anomaly experiment at Fermilab. What's your position? Do you think it's possible this is new physics?
I cannot really judge, but I'm impressed that people are so interested in it. It seems to be there and there's also this ongoing thing at CERN, but it might be more wishful thinking. I'm not sure. But we really need something in particle physics. In a sense, I've been spending so much time trying to think about unified theories, the fundamental theory, the theory of everything which we could say with straight face, way back in the '80s and '90s. Now we have to be a bit more careful. But it's interesting to see that people now are very eager to interpret these two experiments. I cannot really judge it from my point of view here.
Lars, given your unique historical perspective, being involved in string theory really right from the beginning, I'd like to ask at the outset of our conversation, some general questions that I think will punctuate everything we talk about. So, one, in the current vein, is that there's a criticism that at least some branches of string theory have become so mathematical that they really are now decoupled from physics generally, and experimental physics specifically. Do you think that's a valid criticism, and is that even problematic because of the mathematical value that string theory offers?
Well, it is valid in a certain sense because you can overdo things. When I entered particle physics in the late '60s, there had been this great success with using group theory, starting from Murray Gell-Mann's use of SU(3). Particle physicists didn't know anything about group theory at the time, I think, but of course, that's a bit before my time. But then, it was so easy to do group theory as such. You take another group, and you look at representations, and it had nothing to do necessarily with physics. And in a sense, the same thing has happened in string theory. There's a lot of mathematics that you can work on. You can make all sorts of, perhaps, discoveries in mathematics. They might not be so interesting for mathematicians, because they are more interested in general features, not in specifics in some remote part of mathematics.
So, sure, I think it has been overdone in a sense. I think there's also been too many people working in string theory. There was a time in the '80s and '90s when every American university should have a string theory group. They were sort of vacuum cleaning the market for people. That's never good. For a long time, people could survive by reading string papers, and they could then do some twist on it, and that has been a bit too much. We all have to pay for it now because the funding of fundamental physics as such is diminishing and even dwindling. Here in Sweden, it's a disaster. My younger colleagues had good funding 10-15 years ago. Now they're not getting any funding at all from our research council. They are putting much more money into say quantum information. Of course, I've only listened to some seminars in quantum information, but I think they will also follow, more or less, the same scheme. There will be simple problems that they can work on, and then they will get out in various directions. It's not necessarily so but it will be more, again, mathematics of some kind.
So, there's always a problem in theoretical physics that people do what is possible to do instead of just thinking what needs to be done, because it might be too difficult to do. I'm optimistic still, because now there are new generations coming in. They have a much stronger capacity in computing, so they can use very modern techniques to investigate some of these issues that we've been discussing but lacked means to solve. So, I'm optimistic, but it's a bit troublesome at the moment, string theory is not in such a good shape as it used to be.
Ultimately, Lars, do you think string theory is still the best path to developing a theory of quantum gravity?
Yes, I think so. Absolutely, I think so. Of course, I'm biased, but it was wonderful when we realized way back that somehow string theory demanded gravity as part of it. We were so excited because somehow it came out for free. And that, I think, convinced me that this was quite the right way of doing it. So, I do think it is, and I now think this has to take its time. We have to appreciate that we're trying to understand physics at the smallest scales without having any, as I say, intuition how it works at those scales. We can only be guided step by step really by some consistent mathematics within a physical framework. So, I still think it's the right thing to do. I've not seen anything else that would compete with it. Of course, it's a problem because one can say that being so complicated it might be impossible to shoot it down. But that's not the way it will happen. I mean, if we don't get enough results in the end, it will reduce the interest, and people will do other things, as they do now.
Lars, because some people express a lack of patience with string theory, that after 40-plus years, essentially nothing has been found experimentally, to what extent is that unfair simply because we lack the current technology at accelerators that are operating at insufficient energies to see supersymmetry, for example? To what extent is it simply a matter of waiting for the right technologies, or the right budget commitment to come around to prove that these theories actually represent the real world?
It's difficult to say. You mention supersymmetry. Of course, we all believed, most of us at least believed, that one would discover supersymmetry at CERN, at the LHC. And it's been rather a great disappointment that they've not found such particles so far. On the other hand, the energy scale in theoretical physics is sort of logarithmic. So, you never know where you will find supersymmetry. It could be at energies where we will never be able to measure, because I think we are more or less at the limit of what we can do. Of course, we can have bigger accelerators, but then we really have to convince ourselves that we can argue for it with a straight face, and for the moment, I'm not sure we can. So, I think that it's difficult to say. I don't have a really good answer apart from what I've said.
Well, Lars, let's take it all the way back to the beginning. Let's start first with your parents. Tell me a little bit about them and where they're from.
My parents. Yeah, they were Swedish. In fact, people have been asking about my name. It's not so common in Sweden. At some stage, I went to some of these tests to see, and I found out that I'm 99% Scandinavian. No surprise, my friends then said since I am or rather was blond and blue-eyed. My parents came from cities just north of here. They were born in 1913 and 1914 in difficult times. So, they were coming from working class conditions. My paternal grandfather had started working in a fairly big industry in that small city up there and became an expert on turbines. When my father was 15 months old, his father got a cold and was home, and they came from this factory and said he had to come down because there was some problem. He went there, and he got pneumonia and died. So, my father had a difficult— and especially my grandmother then had a difficult time. Fortunately, they had a big house so they could rent it out except for a kitchen where they lived, my grandmother with three small children and a mother-in-law. So, my father had to start working early, and eventually, he came here to work in a restaurant.
My mother was the youngest of 9 children in a big family. She only went to school for 6 years, and the teacher wanted her to continue. I think she was very bright. But she was needed at home. So, they had rather little education, but they were very intelligent people and very well read. At the time when I was born, my father had a big cafe in the city my mother came from. It's called Uddevalla. It was during the war. At the end of the war, he sold it. It was very much work. And we moved here, and for some time he had a shop, and then he went back into restaurants. He spent his life as a waiter in the most fashionable restaurant here in town. He was happy with that. My parents were sort of rather happy people with their situation, which I think many people who grew up in the '20s in Sweden, remembering how difficult it had been after the war, seeing the progress, were. So, yeah, I had very good parents. Of course, they couldn't help me much eventually when I started to study, but they were very supportive.
Lars, did they suffer during World War II, or was your sense that they were largely insulated from the upheavals?
Well, Sweden was insulated to a large extent. The Swedes did not suffer so much during World War II. And especially then, my father had this big cafe. He had access to all sorts of food, so he was even supporting the bigger family in a sense. So, no, Sweden was quite lucky in the Second World War, coming out of it intact, with the industry there to just start to produce. Sweden had a big advantage. It expanded a lot in the '50s and '60s. Sweden was very well off compared to many European countries. For example, neighboring countries that had been occupied like Norway were in very bad shape after the war for a long time. So, it was a lucky time in Sweden, I would say.
Lars, obviously this is before your time, but did you ever get the sense from your parents if they understood the difficulties Swedish Jews experienced during World War II?
There were Swedish Jews, actually even in this small city where I was born. They had started a company there, manufacturing suits and things. I don't think there was any tension at all, as far as I know. I remember in the '50s, I don't think there were any tensions. They were integrated, and then here in Gothenburg there had been a rather big influx of Jewish people in the late 1800s. And of course, there was an influx after the war and just before the war, but not so large. The Jews were mostly very prominent, very important people in town, usually well regarded. So, I have no memory of ever noticing any antisemitism and I had good friends and classmates, and this was nothing that we were thinking about. They were just like any of us, I would say.
Tell me about your early childhood, Lars. What kind of school did you go to as a young boy?
Yes. In Sweden, you usually start at the age of 7. Since I was born very late in the year, I was 6 when I started. I matured rather late, so I was a small boy. I enjoyed school, but I didn't take it too seriously. It was very easy for me, so I was mainly interested in sports and outdoor activities. The Swedish system at the time was such that I first spent 4 years in a common school, and then one could apply to sort of the lower high school. I think we were about 4 people out of 30 from that class that went to such a one. So, that was a huge selection. Sweden was, to a large extent, a working-class society with people not so much aware of higher education, very little academic, I would say. We had four universities in Sweden then. Of course, Gothenburg was a bit different because it was the biggest harbor in Scandinavia. So, there were lots of people working in connection to shipping and there was also ship building. But also, big companies like Volvo, etc. So, I started and then when I got into this lower high school, I noticed it was very easy for me, but I didn't think so much about it. I could read my homework twice and then I knew it by heart. I didn't spend much time on my homework, so I went out playing football instead.
But it went very well. After 4 years in that school, I could apply to a school called gymnasium, which is high school. I applied to the best one in town. There was sort of a real hierarchy in town. It was only for boys, and it was quite competitive. But I had very good marks, so it was no problem getting accepted, and again, it was very easy for me. Then I became a swimmer. I was swimming every day. I thought I would be a world class swimmer, which I didn't become. But then I guess I matured. I had a very happy time at school because it was so easy for me. So, when I got the exam after 12 years, I had very good marks, but I had no idea what I wanted to do because I was interested in essentially all subjects. I was not very good in biology because I was never interested in flowers or birds. Eventually, when I got involved with Murray Gell-Mann, he was getting upset with me when I didn't know even the Swedish names of certain common birds.
Lars, when did you get interested in physics specifically? Was it before university?
That's a very good question, you see, because of course physics was very fashionable in the '50s and the '60s. I was not specifically interested in physics, but here we have an institute of technology, Chalmers, here in town, which was a very good education. It provided the industry with very good engineers, and it was very important in town. They had started a branch called engineering physics. It started in 1956, so it was fairly new, and it was so many boys' dreams of being accepted to it. There were 30 every year. So, I just followed the stream, and I applied to it without too much deep reflections, when I'm thinking about it now. I would say I'm surprised I didn't put more thinking into what I would do, but I was following this dream of others because everyone said if you get accepted there, this is what you should do.
Also, when I finished school, I had a year in the military which was a joke, but it was a year to think a little bit more what I should do. And I guess, I then came to the conclusion this is what I should apply for. So, I applied, and I was accepted. There was one more from my class that went there, and he was extremely ambitious. He was one of those guys, you know, who was running home from school to do his homework, and in the summers, he had a chemical laboratory at home. So, we were the two, and I was the opposite. I was more interested in sports, but I had always been good in mathematics, so I had no problems solving problems. Physics, as such, I guess I was interested in, but not more than other subjects. I was also very interested in literature and languages.
Now I'm boasting, but you have to bear with me, because when I was applying for the last four years in high school, you could choose between the mathematical branch or the linguistic branch or some social one. When my teacher heard I was choosing the mathematical one, he was very upset because he was my German teacher, and I guess I had not made any mistake in German, so he said, "Oh, you should study languages." And I was very interested in languages. Again, I guess because I have a good memory, I could easily memorize all the words. Also, German was especially easy for me because there are these strict rules. I can still tell you which word to choose for certain things, and things like that.
Lars, was it a specific professor or a class that convinced you to pursue physics for graduate school?
Well, graduate school, that was interesting because when I came to Chalmers, to this engineering physics branch, we were 30 boys and one girl, in fact. Then suddenly I got nervous because I'd been having a very easy ride up to that. Here were all these people coming from all around Sweden, and I thought they must be small geniuses, everybody. To my surprise, I realized that I could actually be on top of it. And then, I started to really study hard because this was really tough. We had sometimes 52 hours a week of teaching, laboratory work, etc. On top of that, we would have exams. Altogether, I remember having 80 written exams during 3.5 years. It worked, as I said, very well.
So, it started in the third year. Then we had a big course in quantum mechanics, and it was given by a senior professor. He was a very famous professor. He was a bit shy, but very exact, and he gave wonderful lectures. He was a wonderful person. Somehow, he noticed that I was interested. I was a volunteer in our class to take the notes because since we had so many lectures, someone had to take very detailed notes and distribute to the others. I did that, and then after that, I continued with an extra course in relativistic quantum mechanics. There, we had a new young professor. His name was Jan Nilsson. I might tell you more about him later. He had got a PhD both from Chalmers and from Rochester. He had just come back from having been in Charlottesville for a year as an associate professor, but he went back because he got a professorship in Sweden. He gave this course and was always a good teacher. We were 5 people taking it, and he was very friendly with us. It somehow convinced me, I guess, that I should do my master thesis with him, together with another guy. We were thinking of doing that the last summer but then there was a Swedish experiment at CERN, and they needed some people. I had applied to become a summer student at CERN, but I was not accepted. I realized later on that that was the way it worked at CERN. You had to have someone taking care of your application there, for example, by going through this pile and put your application on top of the pile. Things like that.
So, this guy, Jan Nilsson, he was not that well placed there to do that. I managed to do it myself later which I have to admit. But then we went down and worked on this Swedish experiment for two months, and I loved CERN. Then, it was clear that this is what I wanted to do. So, I finished the fourth year, I finished it after six months, and then I would start doing graduate school immediately. We didn't have graduate schools in the modern sense at that time, because what was happening was that this was still the old Swedish system, which was like the German system, that in order to get a doctor’s degree, essentially what you had to do was just to write a thesis. We did have courses, but we were few graduate students in particle physics, and mostly one had to read books, and then go to the professor and have an examination of it.
So, this is what I started with. I tried to start it exactly when I finished, but then I had worked so hard, so I took the summer free, and I started in the fall of 1967. I then realized how the system worked. There were other graduate students because there were five professors in the department. But the way they did it was to say, well you work on some problem and eventually Jan Nilsson said to me, "I think you should work on phenomenology." He got me in contact with an experimental group in Stockholm to work on proton-proton to proton-proton pi+ pi-. It was a bit of a shock to start with the graduate studies, because I was very much alone then. They only introduced graduate schools a bit later.
So, eventually when I got my PhD it was in the last year one could get the old type of degree. After that, they turned it into a modern doctoral exam, more like the American system. From that point of view, I more or less learned how to study particle physics on my own. I was reading books, and I was not very happy. I could see my friends from my class going out in the industry, and they were getting good salaries, but they had to move around in Sweden. I could stay home and continue. I was, of course, working quite hard on my own trying to educate myself. We had a few courses, I would say, that were common for all graduate students, statistical physics, and quantum mechanics. There was a big one in quantum mechanics. But most of the time I was sitting there at the desk or going to the library trying to find books. I didn't get much help from my advisor. He was always somewhere else, also. So, that was a bit hard.
Lars, given how much you were reading in the library, in the late 1960s and early 1970s, did you have an appreciation of all of the exciting developments in particle physics elsewhere in Europe and in the United States?
The funny thing is, which I don't understand now, is that during the first semester, I don't remember now how it worked, I came to read those papers which were on what became duality. It was first a paper by Dolen, Horn, and Schmid. They argued that if you write an amplitude, you need to do it either with what's called Regge-poles, or you could do it with intermediate resonances, but you should not use both at the same time. That was a big surprise. And somehow, I studied that on my own. I even gave seminars on it in the group, and I was following it. And in 1968, Gabriele Veneziano announced his paper. There was a big conference in Vienna in the late summer of 1968 or beginning of the fall. Somehow, I was prepared for that. I could start to study it, and I was very lucky with that because somehow, it became very relevant in my rather random search for papers to read or books to read. Of course, I had big gaps. And of course, then there were the summer schools which were very important.
In 1969, I went to Erice, and that was wonderful. We were there for two and a half weeks or something, and there were very good teachers. Shelly Glashow and Sidney Coleman were there. Murph Goldberger was there. And there were lots of students from the United States, from Italy, France and England. I think we were three from Sweden. And there was also a guy from Denmark who had just made a great success, named Holger Bech Nielsen. I can back up a little bit, because in June of 1969, there was a big particle physics conference in Lund in the southern part of Sweden, where I was drafted as a scientific secretary. So, I was there and there was a big session on dual models, as it was called then. Veneziano spoke, and others. There were essentially just young people doing it.
But the main attraction was Holger Bech Nielsen. He was very different, I shouldn't say funny, but a very interesting guy. He was small, a bit round, he was dressed in a suit with a bowtie. We eventually joined forces at CERN later on. He could have this suit for a week or so, and then it was so dirty that his mother had to clean it. But he had together with Koba, written a very famous paper, the Koba-Nielsen paper, which gave the N-point amplitudes in dual models, a beautiful formula that they had devised. So, he gave this talk in Lund, and he talked in a very loud voice. You have to tell me if I talk too much, but he was coming from the Niels Bohr Institute. Eventually, he became the famous professor of the Niels Bohr Institute.
You know, at that time, you had a microphone, and you had a long cord, and he managed to turn around, turn around, and getting the cord around him, and eventually he couldn't move, but he didn't notice it and he was still talking loudly. It was hilarious, and he was such a wonderful person. Of course, we always thought he was the genius of our generation, and in some respect, he was. But we can come back to him later. So, he was also there in Erice. Then I got to know him a bit better. So, it was very important and useful for me. In the year after, there was a meeting in Copenhagen. I was only there for a week, and I'm not sure I learned very much because the big attraction was that Nambu was supposed to come, but he didn't come because his car had broken down. He had been driving from Aspen to Chicago when the car broke down, and he had to stay somewhere, so he didn't make it. But his manuscript made it, and we all got it. I think he had probably typed part of it himself, because he had misplaced his fingers. And that was a wonderful paper. I remember I got it and I was studying it very hard. This is where the Nambu string came from. He wrote the action for the string, just as an exercise.
So, in that sense, I did have contacts with the external world. Also, what was good was that my advisor, even though he was not so active himself, had lots of friends that came by and were staying often for a few months. He was clever. Later on, when we had moved around in the group, he had put me in a big room with an extra desk, and often I had some visitor there, whom I started to collaborate with. So, this is the way I started to write more papers. I did finish eventually the analysis of that experiment, but after that I started to work with some of his friends, mostly on weak interactions.
But I should also say, he did another good thing for me because he happened to be on sabbatical in the year 1969. In the fall, he was in Texas. They had set up a more or less new group there with George Sudarshan, who was Jan Nilsson's close friend. And Yuval Ne’eman was there, so it was a very interesting group. I was there for a few months, and we were supposed to work on some group theoretic issues that Jan thought were interesting. That didn't work out, but again, there was always a flow of people coming in to give seminars. Even Nambu was there to give a seminar, so that was helpful. So, I could keep up a bit with what was happening.
Lars, when did you first become aware of first Veneziano, and then later on, Schwarz and Green?
Oh, yeah, that would come later. Veneziano, of course, we heard about, and then I saw him, as I said, in that conference. In 1971, I got a fellowship to go to CERN. That was before getting my PhD, but the Swedish system was a bit different from the other European, because in Europe they had modernized graduate schools, and they did not have the old system where you had to wait long to get your PhD, except Denmark, where my friend Holger Bech Nielsen never got a PhD, but he became a famous professor anyhow. So, I came to CERN. They had realized that I was in a place that was not very useful for me. So, somehow, they allowed me to come already in June, for two years. I came there and after a few weeks, Holger Bech came down for a short visit. There was also a visitor visiting CERN for five week or so, that he introduced me to. And that was John Schwarz. The first two months I was at CERN alone, and then my wife came down.
But so, the first two months, I was spending all the time at CERN. It's interesting when you look back on your life, you see that there are all these coincidences, in a sense, that shape your career, because I met John in this way. John was really a rising star. He had constructed the Neveu-Schwarz model. He was at Princeton at the time. So, we became good friends. It's not that we discussed too much dual models, because I was not experienced enough to discuss with him. I noticed very quickly when I came to CERN that I had big gaps, and I again had to study a lot of papers. But I knew what to study, which papers I had not read, etc. Since I was eating all the meals, and I was spending a lot of time with John I learnt what was new. I also had a car, so I could drive around with my new friends in the weekends. So, we became good friends even though we were not close to collaborate. CERN was a wonderful place in those years, especially the theory division.
The first of July David Olive came. David Olive was one of the Cambridge four, as they were called. They had written a very famous book on S-matrix theory. He had given up his lectureship in Cambridge to become a staff at CERN, a five-year job, which was brave and a bit naive because he believed that he would be able to go back to his lectureship. In the end, it was not so easy. Anyhow, he was there. David Olive was a wonderful person. Extremely sharp, clever and very soft-spoken. In my office in Chalmers, I have a big poster in olive green that is a copy of one I gave to him when he was 60, which says, "There must be a better way of explaining it." That's what he used to say every time. Many people got a bit offended, but I didn't. He was always right about it. So, then I had that contact.
Then, in the group of people that came a few months later as fellows, I got another roommate which was Joël Scherk. He was young. He was 25 coming from Paris. He had already made a name for himself in dual models. He was in fact invited to come as a fellow. He never applied for it. He came, and he was sitting opposite to me. He was a very different person. He had long hair, which was unusual in the theory division at the time. Fancily dressed, very soft-spoken, but again very, very nice. Very good. So, it was all set for me there to have good friends and good people around. And later on, Holger Bech came down for a longer period. So, we started to work. In that summer, there had been a stream of people passing by the office, so I wrote a few papers with them, which are completely forgotten. But when Holger came, we realized that we were a bit behind in dual models. So much had been done during the year before, and also during that year. That was the year when it was proven that there were no ghosts, no negative norm states in the theory. And there were very many people in this dual model group.
There were probably 15 people when we had special seminars, just discussing the latest papers. Well, Holger and I wanted to set up to see if we could find a realistic string model for hadrons. This is what I mentioned in the beginning that I'm still thinking about. We actually made some progress, but it was eventually a few years after that we published it, because Holger easily lost interest and then started on something new. And also, as I said, the year after QCD came, and then it was not so interesting. People were not interested anyhow. But it was in retrospect a very interesting idea actually, the paper was better than I thought at the time. But we couldn't have done much more then because the problem with it is that we were so strongly believing that the hadrons should be described exactly by strings. I realize now is that it's more of a framework, it's a certain approximation, but you should still be able to use the techniques, and you should be able to get all sorts of connections from that idea. But one has to give up some of the very strong constraints you put on amplitudes. And we didn't do that, so we were a bit disappointed. So, we spent a lot of time on it during that year.
After one year at CERN, I'd written some papers, but I hadn't been too successful, I would say. During my second year I started to discuss with David Olive. I was feeling lonely, and he was also a bit left alone. He had had a graduate student from Cambridge working with him the first year he was there. We decided, or David probably said, let's try a difficult problem. Let's see if one could construct consistent quantum corrections to the amplitudes in the dual models. People had already tried to do it. There was what was called an operator formalism where you could construct scattering amplitudes, and you could take a scattering amplitude and sew it together, and then you would form a loop amplitude, a higher quantum correction, but they were not consistent the way they did it, but still, this is the way that Loveless got 26 dimensions, as a fundamental dimension of the bosonic string theory. But we wanted to do it really carefully, and this was the sign of David.
So, we started to study how to do it. We knew at the time that string theory was a more complicated gauge theory, so we tried to copy how it works in Yang-Mills theories. Gerhard 't Hooft had come to CERN, and we studied his papers very carefully, and we were discussing with him. We were working for six months before we found the right technique to do it. And the way we did it was to go back to a paper or rather a conference report that Feynman had written in 1963. This is where he introduced the ghosts, which then went under the name of Faddeev-Popov ghosts because they were in the audience, and then they had somehow understood how Feynman had done it and written it up. We could recreate it. We constructed a projection operator on to the physical states, that if you put it in the scattering amplitudes in the lowest order, it was just one. But it did not give one in the naïve loops. We could see that it really only worked in 26 dimensions. When we put it into the loops, we could compute its effect and it gave us the correct result.
So, suddenly, it opened up for us. I think I wrote 8 papers during my last six months at CERN. One of them was another paper when Holger Bech came down for a week, and he told me, "I know a way to get 24". 24 is the number of transverse dimensions in 26 spacetime dimensions. We realized that if you have a string, there's an infinite set of harmonic oscillators. So, every harmonic oscillator has what's called a zero-point fluctuation. So, if you sum up these zero-point fluctuations, you get an infinite sum, and that infinite sum is infinite because it's essentially the sum of all integers from one to infinity. We realized that we could renormalize that, because these waves travel with the velocity of light because there are no other parameters. So we said, “Let's renormalize the velocity of light,” and then we got a finite answer, and we got the sum of all integers to be equal to -1/24, not knowing that it was a famous result going back all the way to Jacobi, as it turns out.
We now had another way to prove that the string only worked in 26 dimensions. So, we could easily write a paper. We wrote the paper in 3 days. That was rather revealing. It was nice. Anyway, when I went back home after 2 years, I'd written 12 papers during my time at CERN. I was very happy. I had had enormous luck, you know. I met the right people and had been there at the right time and I had got interested in problems that somehow suited me. So, when I came home, I wrote my thesis for the doctor's degree.
Lars, was the thesis paper a combination of all of these papers, or did you focus on one particular topic?
No, no. Yeah, there should be sort of a line through it, but I put together 14 papers, which was sort of a record. I was very ambitious. And then I wrote a hundred pages as an introduction to that.
So, Lars, what was the through line? How did you synthesize all of these ideas into the thesis?
I don't even remember, but most of them were on dual models, or scattering amplitudes, and strong interactions. I had written, as I said, some papers on weak interactions, but I left them out. I took essentially all of the others. I think one criterion was that they should have been published in a journal. So, this is what I did. But coming back to Sweden was pretty tough because we had had a wonderful time in Geneva during these two years.
Lars, do you have a specific memory of when the term string theory started, or who even coined it?
Yes. Holger Bech always talked about string theory, but it really goes back first to Nambu, who in a famous talk somewhere in 1969 said that this looks very much like a relativistic string, when you look at the spectrum of the Veneziano model. Of course, Lenny Susskind was also very quick on it, and if you talk to him, he will say he had the idea first, certainly. So, usually we credit Nambu, Susskind, and Nielsen. But the Cambridge people were not too keen on it. They were living in an S-matrix world. They were looking at scattering amplitudes. So, David Olive never during those years would mention string theory, but he was still thinking about it as more like dual models or scattering amplitudes.
And also, Peter Goddard, who was another fellow there at CERN doing important work would not, until he did some groundbreaking work on the relativistic string with Goldstone, Rebbi and Thorn. John Schwarz was not very interested in it in the beginning. He was also coming from the S-matrix world. He was a student of Geoff Chew in Berkeley and had worked on S-matrix theory before dual models. So, people did not talk much about strings. When I came back to Sweden, eventually I got one graduate student, so that was my group. I gave him a problem. We had strong withdrawal symptoms as many people had at the time leaving CERN.
Lars, was your professorship put together before you even defended your thesis? Was that already set?
No, no. I was some kind of research assistant. It was a rather low-ranking position with the research council. Then, I got sort of a recruiting academic position after a while when I was back. But the criteria for that was that one should not be what's called a docent, which is an honorary title you can get if you have a successful dissertation with a good mark. So, I applied for that position before I became a docent, and eventually got it, but people complained that I was overqualified for it. There was someone, and he went all the way up to the government to complain, who decided that I was overqualified, and the other guy got it. He was five years older than me or something, and he was not overqualified. That was Sweden at the time. So, I was having low-ranking positions, but I was treated well. That was not a big problem for me. But there were no professorships to apply for. Professorships had to be announced by the government at the time. So, that took to the '80s before I could apply.
Lars, when did you start thinking about supersymmetry?
Yeah, that's also a good question, because somehow, we did do supersymmetry early on. We did do the supersymmetric version of the string. So, we were certainly thinking about it already back in '72-'73, but then another of these nice coincidences happened. You have to have nice coincidences happen to you if you are in a small place. There was a Nordic institute for theoretical physics in Copenhagen, Nordita. Paolo Di Vecchia, an Italian, came there as an assistant professor in 1974. He had also been a fellow at CERN. He came to CERN half a year after me. I had not discussed much with him there, but we became very good friends. Nordita had a good budget. The idea was that they should work for the whole of the Nordic community, especially more so in Norway and Finland where people were very scattered, and the only chance they had to meet other people was to go to Copenhagen.
Paolo was organizing meetings, and eventually we started to work together. We set the goal to see if we could find the corresponding action for what we called the supersymmetric string, which is the basis for the Ramond-Neveu-Schwarz model. Already from the beginning, I had the idea that we should try to use Grassmann variables. Somehow, I got interested in that very early on, so Paolo and I started to see if there was a way of just taking the Nambu action, which is of course in terms of spacetime variables x, and you add what we called theta, anticommuting coordinates. We were struggling and we were not making much progress. We were working for a year, and then I think in 1975, we found that we could do it, in a less ambitious way. We could do interesting things not knowing the general action. By doing that, we even discovered two new supersymmetric string theories, which in the end have not been so useful. They are still around, but we also found new ways of doing Virasoro algebras.
So, I got even more interested in supersymmetry, and I also realized that in the Neveu-Schwarz model if we introduced these anticommuting coordinates, I could rewrite the operator formalism in a beautiful way. We had a meeting in the summer of 1975, a string meeting in Durham, England. I got the idea, and I was sitting in the library sketching it. When I got back, I wrote it up with the student I had at the time. So, in that, we also realized how to do what's called super conformal algebras, which people had not done, and people wouldn't do for another ten years. It was there for 10 years before anyone rediscovered it, and they were not happy when people pointed out that it had already been done.
Then, another lucky thing came. I should have said that in 1974, I went to Aspen. John Schwarz organized a workshop there. That was wonderful, so my wife and I went to Aspen for three weeks, and we were sold on Aspen. Most of the people still doing dual models at the time were there. Pierre Ramond couldn't come, and I had still not met him at the time. But other people came. There was another workshop on gauge theories, and all the famous people were there. It was wonderful to be in these activities but a bit intimidating, but it was really great fun to be there.
Did you interact with Feynman at all, Lars?
The funny thing is that that summer in 1974, in Aspen, that was the only time that Feynman came to Aspen. He was just walking around, talking to people, but I don't think he was feeling very much at home there. Murray Gell-Mann had a house there, and he was sort of at the center of attention. Feynman was walking around, and the day when David Olive gave a talk on our work, which was based on what's called Feynman’s tree theorem, as I mentioned before, which he had just sketched in the talk in Poland, then Feynman came into the patio where the lectures were and looked at the board. That was the only time I could see David Olive get red! When we had written all those papers at CERN, David Olive and I, and extended the group to also Joël Scherk and Claudio Rebbi we used mostly the projection operators but the first two were essentially using Feynman's tree theorem.
Somewhere in the beginning of the summer of 73, we got a letter from Feynman, starting, "Gentlemen, I've been reading your paper …." and then he was praising us. I still have it on my board in Chalmers. It was wonderful. I even used it when I was applying for jobs. Of course, we didn't dare to send the paper to him, but John Schwarz had then moved to Caltech, and had shown him that. Aspen was the first time that I saw him. The next summer in Durham when we met, the summer after Aspen, many of the people who had been at that meeting in '74 did not come, partly because it was Europe, partly because string theory was at the bottom, so to speak. But the other important thing that happened was that one person came, and that was Pierre Ramond. I've been telling this story a lot of times, but it's actually true.
So, he comes there, I get introduced to him, and he said, "Oh, my god Lars Brink!" So, usually I say, "Well, someone who calls me his god, he must become a good friend of mine." So, I met him there, and we immediately became very good friends. But another thing happened in that fall— We wrote those papers on new string theories, and involved an enormous number of Italians into the collaboration. I had decided that I wanted to go back to CERN for a year in '76. I was sort of timing it because we were getting our second child, and it would be a good time to be in Geneva. Then I got a letter from John Schwarz wondering if I could come to Caltech for that year. They had some opening and offered it to me. So, of course, we did that. We couldn't be there for the complete academic year, because my wife had to go back to work. But we spent 7 months at Caltech. Pierre Ramond came also at the same time, because he was coming on a rather loose position as Murray Gell-Mann's research associate. He had given up an associate professorship at Yale, a non-tenured one, just to go to Caltech. So, that's the way I came to Caltech in '76.
And is this where you started working with John Schwarz and Joël Scherk on supersymmetry?
That is true. Actually, John had written to me when we had written the first paper on these new models and new algebras in 1975. We had then constructed amplitudes for all of them, and we were writing it up. Then, John wrote that he had appreciated it much and that was what he had looked for, for a long time. He had also constructed the interacting model for the simplest new model. So, we said, "Why don't you join our paper?" So, that paper was me, John Schwarz, and 11 Italians.
Then, before I came to Caltech, there was another thing happening. We still wanted to construct the action for the superstring. In the beginning of the year, supergravity had been discovered, and eventually we learned about vierbeins and how to have fermions in gravity theories. We then realized that this was what we had missed all the time when we were trying to do these things. So, in the summer, we wrote a paper which was sort of the classical paper for a Dirac particle, since when you quantize, it gives you the Dirac equation. We knew then how we should do it for the string. But I had to prepare for going to Caltech, so we decided that in September I should go down to Copenhagen to Paolo for a week. We were working day and night to really check this action, and we got it. It worked. We did it with a young English guy who was a postdoc there called Paul Howe.
Lars, what was the intellectual process of recognizing the significance of Yang-Mills when you're thinking about supersymmetry?
Yeah, yeah, but let me just give you one more. So, the first thing, when I came to Caltech, John said, "Did you write down the action for the N=2 model, the new string theory?" "No, we did not have time for that." "Let's do that," he said, and he put me in his office. I was jet lagged. I was setting up the family and were renting a small apartment in Pasadena that was furnished but we had to find various household equipment and such stuff and stuff for the kids. They were two small kids adjusting for the jetlag. But we worked very hard, and in a week, I had my first paper at Caltech with John. After that we said, "Let's go over and check supergravity." And we had an advantage because we were used to be working in ten spacetime dimensions and we wanted to use that. At some stage, we said, "Let's first construct all the possible super-Yang-Mills theories. And we did it. We started in ten dimensions and went down to 6, 4, even further down. And again, we worked very hard. When we were done, we wrote this up and John just got a letter from Joël Scherk, saying that he had also worked out the maximally supersymmetric theory in four dimensions in another context. So, John said, "Well, let's put your name on our paper" So, this is how that paper came about. We were proud of it, but in the end, nobody else cared about it.
When we talked about higher dimensions, we had to be very careful to say that this is just a technique. We're not thinking of 10 dimensions as real dimensions. Even Murray Gell-Mann was very strict on us, saying, "This is a technique." So, after that paper we were struggling, and then eventually I said that I'd been quite successful using the anticommuting coordinates. Let's do supergravity also in terms of these Grassmann variables. So, we started doing that, John, and then Pierre came in, and even Murray was interested. He was interested in supergravity because he wanted to really see if it could be used for grand unified theory.
So, then, the four of us worked it out, and we wrote 3, 4, 5 papers on it. I was on 3 papers. But those were not so earth shaking. But it was wonderful to be at Caltech and in Pasadena, but then we had to go home in the beginning of the summer. Of course, I was scared to discuss with Murray in the beginning. He was formidable. Did you ever meet him? You are too young to have seen him in action. He was completely fantastic. He had the world's best memory. I have a good memory too, but I couldn't compete with him. We could discuss on my terms, you know, and he liked that. Somehow, he liked Europeans. That's one reason he liked Pierre so much too, I think. Not only that of course, but that helped because then he could try also French expressions and the French history and all those things, and with me it was Swedish words. He could test them. So, when I had to leave, he said, "Please come back. You can come back whenever you want."
That was typical for him. He didn't care whether there were resources for him. But of course, he had lots of money to invite people. So, I said, "Okay. I will try to be back for some time in the fall." I did that. In the summer of 1977, there was a seminar in Aspen where someone was talking about the N=4 Yang-Mills theory, and they showed that at the one loop level, what's called the beta function was 0. That means that you do not have to renormalize the theory to that order. Murray then said, "Oh, it's probably 0 to all orders." Of course, he never wrote it down. He would never ever write down a conjecture like that, because he had to be absolutely sure that what he wrote was correct. He commissioned someone to do the 2-loop order. Just when I came back to Caltech in the fall, there was this guy called Poggio from Brandeis coming to give a talk about the 2-loop beta function and showed that it was zero, and then the race was on for the 3-loop. But I didn't want to join that, so John and I were still for some time discussing supergravity.
Then, this guy called Paul Howe, whom I'd been working with in Copenhagen for that action, came to me as a postdoc. We had a few postdocs in the department, and in 1978 I could hire one. So, I got him to come, and eventually, in 1979, we took the work done with John, Pierre, and Murray, and went all the way up to N=8 supergravity, the maximal supergravity in four dimensions, and we could formulate it in superspace. That was useful work because then one could really argue if the theory was unique, and things like that. Paul and another guy checked whether one could construct counter-terms. They found that it could be that N=8 supergravity was finite all the way up to 7 loops, and this is still a result which has not been disproven. People have been up to 5 loops and checked it. So, that was useful.
So, I was very much involved in this N=8 supergravity from that point, but I kept contact with John. I went to Caltech every year for some months. But John also teamed up with Mike Green around that time. John knew Mike Green from Princeton in the late '60s. The first time I met Mike was at CERN actually, when I was back for a conference in September of '73. He was also in Aspen the summer after. Mike and I tried to overlap at Caltech, but he did not have a family and could stay on for longer.
Lars, in thinking about supergravity, when did you become aware of Dan Freedman's work?
First, you know, Freedman, van Nieuwenhiusen and Ferrara published their work I think in March of 1976, and just before that I was at CERN for a few weeks, I think in the end of February of 1976. There I talked to Bruno Zumino, and he told me that he and Stanley Deser were working on a theory with spin 3/2 and gravity. But all was very secretive, and soon after that, the Freedman et al paper came, and I learned more about their work because Ferrara was working with us on those new string theories at the same time. So, I was surprised that he was also on that paper, but he had gotten into that collaboration quite late, but made some substantial contributions to it. If you really look at the preprint, you will see that his name is a little bit tilted. They glued it on afterwards. We then used this technique in order to construct the action for the string theory. This actually later became known as the Polyakov action, which Polyakov hates that it's called that.
There's another of these funny stories. You can erase a lot of what I'm saying, but just before, when we had just done this action in 1976 in Copenhagen, there was this Russian guy who had just arrived, and that was Sasha Polyakov. He had become extremely famous during that summer because of what's called the instantons. So, I just met him, and he heard that I was going to Caltech, so he gave me a handwritten manuscript. That was about quark confinement in three dimensions, which he had in principle solved with instantons. And I brought it and it was studied very hard at Caltech at the time. Murray, one day, came to me. I had only been there for a month or something. He said, "You know this guy. Can you call him and tell him that we want to invite him for three months? Use this credit card."
So, I went up very early one morning and called Copenhagen, got hold of Sasha, and told him that they want to invite him to Caltech, and he said, "Whatever my official reply will be, you should tell them that I would very much love to come." He managed to come a year or two later, and then he saw the paper that John and I had written and realized how to write actions for supersymmetric strings. Later on, he quantized those actions and made some beautiful work with it in 1981. So, that's when it became known, and that's why it was called the Polyakov action. And of course, coming back to Freedman, he became a big shot after supergravity. He then moved from Stony Brook to MIT. He spent a year at Caltech at some stage, late in the '70s. He was all the time working on supergravity.
Lars, tell me where you were in 1984 when all of the excitement with the Second-String Revolution happened.
Yeah, yeah, yeah. Okay. As I said, I was going to Caltech every fall for one or two months, and we were meeting, John, Mike Green and me. We were working on string theory in the fall, and then we were back at doing supersymmetric field theories in the spring. But then— I have to back up. In 1982, I suddenly got a very good idea. I'd realized how to prove that N=4 Yang-Mills was a finite theory. So, I got very excited. I had two graduate students. One of the guys had really graduated and he was waiting to go for a postdoc. We were working in the summer, and we were putting it all together, first to construct it anew in what is called the light cone gauge. I was confident that nobody else had ever been thinking about the same kind of formalism for this theory. So, we were a bit nervous about making mistakes.
So, first we sent out the paper with the formalism, and then we would work out the details of the final proof, doing it very carefully because we were not real experts on Feynman diagrams. I had given lectures on quantum field theory which is very useful in order to learn all the details about Feynman diagrams, but not worked much on it. Then there was a conference in Paris that summer, and Stanley Mandelstam announced the same result as we had. His paper came out a bit earlier than ours, but we got our paper together very soon after. When I came to Caltech in the fall of 1982, I went to Murray and I said, "Look, I proved your conjecture that it's finite." He said, "Oh, but you must have a scale in the theory." After that I was touring the world discussing about the finiteness of N=4. In the summer of 1984, I had an offer from CERN to be there for the summer, and then the question was whether I should go to Aspen or to CERN. John and Mike were going to Aspen, and I took a chance and chose to go to CERN as it was good for the family to go to Geneva. They liked to be there in the summer. So, the answer to your question is that I was in Geneva for the summer, and when I was giving lectures at a big summer institute in Bonn about superstring theory, I got the news that they had proven that it was anomaly-free. That was, of course, shaking up the whole world, you know.
And this is of course when Ed Witten takes notice.
That's when Ed Witten comes in, yes. That's true. Yes, and the world changed. I came to Princeton in the winter. By the time, I had a pretty big group at home. I had many graduate students and with some of them we were working on a paper. We wrote a paper where we could argue that the superstring theory is at least a renormalizable theory. That we could not say about gravity. So, that was a step forward. There was this important problem if the superstring theory is even a finite quantum theory, even though it has a dimensionful coupling constant. So, I came to Princeton and that was also after the heterotic string, with David Gross and other people and the Calabi-Yau solution with Ed Witten and collaborators. When I gave a talk in Princeton, the lecture room was full. People were standing in the corners. That seldom happens.
So, there was so much excitement. We then had a huge summer workshop in Santa Barbara in the institute in '85, and almost everybody was there. The summer of '85 was so hectic. I went from one school, one conference to another, and there was a big Les Houches meeting in the Alps. It's a summer school where students are there for several weeks. I was there for two weeks, and I was giving lectures about superstrings. Once I was lecturing up to 12 o'clock at night, because they wanted to have more and more, and I was exhausted. I had to go back, and I went back home one day and then I went straight to Santa Barbara to that workshop there, and I gave a talk already the first morning. I wonder how I managed with the jet lag, but somehow, I did it. Of course, it's hard to imagine what kind of excitement it was during those years.
Lars, why specifically? What was the reason to be so optimistic? What was thought to be on the cusp of discovery?
I think it was two-fold. One was that this is really a chance of getting a theory which is a finite quantum field theory involving gravity. And the other thing was that one could possibly find the grand unified theories within a system which also involved quantum gravity. Grand unified theories had started with the SU(5) theory, which was back in '73-'74, and then the SO(10). But then there were all sorts of such models at some stage, I don't know how many on the market. There's still a problem that you cannot exactly pin down what is the grand unified theory, and there was a great hope that by understanding the right internal space in Superstring Theory, you would get the exact number of generations and the right gauge groups, etc. So, that looked very promising. I was always worried about that though. It looked very unique when you are in 10 dimensions, but there were zillions of ways of taking those theories down to 4 dimensions. So, I never dared to join those searches and I never had the mathematical knowledge and skill to do those things. Of course, Ed Witten was so much ahead of everybody else doing those things.
How so, Lars? In what ways was he ahead of everyone else?
Well, because he understood mathematics in a much deeper sense than anyone else in the business. At the same time that he was the best physicist, he was the best mathematician in physics. He was even one of the leading mathematicians of the world. He was so impressive. He took over the role that Murray Gell-Mann had had in particle physics in the '60s, well, starting in the late '50s, through the '60s, beginning of the '70s. After him 't Hooft had been sort of the leader in the '70s, and then Ed came. He came with this new mathematical insight which scared lots of people. It scared Murray so much that he almost left. Well, he essentially left physics to do other things. So, even though he's a very nice guy, he's very different from the generation of Feynman and Gell-Mann. He's a rather unique person. People ask whether he's coming from Mars or some other planet.
Lars, and then, yet again, in 1994-1995, there's more excitement in string theory. What was your involvement at that point?
Let me skip the discovery of M-theory since I was not so involved and go to a few years later. That one, that explains this discussion I had had with Murray Gell-Mann, where I was so proud to say we've proven that N=4 is finite, and he said, "You must have a scale." What Maldacena proved was that you have to interpret the N=4 differently. This was in ‘97, ‘98. Since it's a conformal field theory, you have to look at conformal weights etc. Then you have scales and it can be connected to superstring theory. You have this duality. Which is an absolutely fantastic idea. I'd always been worried about the strong coupling limits because when we do quantum field theory, and when we compare with the data, it's a perturbative theory with small coupling constants.
But for these theories, this is just a tiny bit of the theories that we are investigating. Almost measure 0 of what the whole theory can contain. But here, certainly, you could see that even though we might not be able to do N=4 Yang-Mills theory at a large coupling constant, we could still get results from a small coupling constant in the supergravity theory in one dimension higher. I think that was such a brilliant idea, and a brilliant result. It's one of those results that really make you believe that there is in the end some kind of simplicity in basic physics. These fundamental theories contain the ingredients for the whole thing. It's just a matter of interpreting them.
Lars, are you talking about the kind of simplicity that Einstein believed existed below quantum mechanics?
No... I don't think it's that. I think this is one step further. I don't know if it's ahead, or aside. It's just that you can build physics by setting up all sorts of small theories. Particle physics started like that too. You do simple models that would explain a phenomenon, and if it didn't explain the next phenomenon, then you enlarged the model. Eventually you will find that if you just look at 4-dimensional relativistic many body theories, it has to be a Yang-Mills theory of some kind, which I think is a very important result. And then you can ask, if you have the theory that is describing what you're measuring at CERN for the moment you have to consider gravity too. You have to take that into account. You have to have quantum gravity. And quantum gravity turns out to be very complicated. If you want to do perturbation expansion in gravity, or in supergravity, you run into enormous numbers of terms. You must have heard that, when people are studying perturbative supergravity just to prove that there are these results you have to find new ways to attack the problem.
There's a group around Zvi Bern in UCLA, and his collaborators that are specialists in computing higher order corrections in many fields, but also in the N=8, the maximum supergravity. We had a technique actually, starting from string theory. In fact, it started from a paper that John and Mike and I wrote where we did it at the first loop order. We used string theory because in string theory there is only one higher loop correction at each order and then you have to take the point particle limit. Then, when they did the 4-loop, they said it corresponded to calculating 1026 Feynman diagrams. With their techniques, I think they were down to a few hundred terms. That amounts to enormously complicated diagrams and integrals to check.
What I mean is that if you dig in these theories, and you do it the wrong way, you find that there are so many terms. It's impossible to solve them, but there could be a completely different way of attacking the problem. In this process we have seen that gravity and Yang-Mills, and the Superstring Theory, containing both of them, are really strongly connected to each other. In a sense they are parts of the great scheme. In some sense they may be the whole thing if we understand them fully. I don't think that Einstein would have liked it, but somehow, how should I say? I'm so optimistic in a sense, even though I will not be around to see it. But 100 years from now, when fundamental physics will be understood at a much deeper level, there will be much more unity. There will be all sorts of ways of getting results from something which we are able write down that is this ultimate theory.
Lars, if the SSC was built at the energies that they were thinking about at the time, do you really think we would have to wait 100 years?
That's a very good question. I think it's impossible to say. As I said, the problem is that theory grows logarithmically. Experiments grow exponentially, I mean in cost. So, that's why they meet too quickly. But in the end, I think that somehow theory should be guiding us. Of course, we have to use experiments, physics is an experimental science, but in the end, I think we have to take some leaps in theory, in the mathematical understanding. My hope is that we have the Superstring Theory, we have super Yang-Mills theory, they are the basic ingredients, and it might be that it's just a matter of interpreting things correctly, using them in such a way that we can get out results which we can somehow read off at higher energies. Then, we'll be able to fit the data which we get now, because already we fit all the data at CERN, it seems, with the existing theory.
But of course, there will hopefully be coming new accelerators, and we will see new phenomena. So, I think the picture will eventually be so beautiful. I'm very optimistic that we somehow one day will say this is the basic theory of the world. Of course, there was a time back in the '70s when we went around and said that if you can only understand quantum gravity, we would probably find that there is only one unique possibility, and then everything would follow from that. That's, of course, very naïve. In the end, I don't believe that any longer. But I think that somehow this framework properly interpreted with new mathematical insight will pin down what the basic laws of nature are, which would be very beautiful to see. On the other hand, it's not at all modern these days.
As I said, the research council here is not very interested in it. It's partly our own fault. I think we gave them too strong words that we would be able to solve it in our generation, etc. Of course, things don't work that way, but I think this is very important that we continue to do it, and there will be times when nothing happens, and then a revolution will come and we'll take it a step further. So, like when Maldacena brought in the duality, it was not that we brought in new models or new mathematics, the idea was to interpret existing models differently, which allowed us to see many more relations. So, my hope is that in the end we will see that we will have this framework where in principle we can say that these are the basic laws of nature. Now I'm getting very philosophical.
It's inevitable to get philosophical when thinking about these things. Lars, tell me about the circumstances whereby you were elected to be a member for the Nobel committee for physics.
Yes. Now I have to be very careful because part of the work is very secret, and part is open. I was elected to the Royal Academy of Sciences here in '97. There are 18 working members in physics, but then you can stay on after retirement. And within that group, we choose 5 people to be members of the Nobel committee. There could also be adjunct members, so in the beginning I became an adjunct member. That group is then doing the work, the necessary work to be able to propose who should get the Nobel Prize for a certain year. Of course, one has to have some kind of fairly broad representation within this group. So, in a sense, you could say that I represented particle physics and mathematical physics. The big fields should be represented.
How big is the committee for physics? How many people sit on this board?
Well, as I said, 5 ordinary members, and there would be one or two adjunct members who are also working as full-time members. It's just a way of introducing more experience and knowledge, because physics is much broader now than it was 100 years ago.
Lars, can you talk a little bit about the nomination process? Is it only a matter of receiving nominations, or does this 5-person group go out and consider people proactively?
What's happening is that there is a rolling scheme to try to cover all universities, more or less, in the world, and send out letters to deans of physics, and chairmen, etc., to get lists of the physicists there, and then to send out letters asking them to nominate. But then, it's also important to find people in physics institutes, etc. So, there's an active way of trying to cover the whole world so one should get as many nominations as possible.
I wonder if you can comment on the Nobel decision not to recognize advances in theories that have not been borne out experimentally. In other words, there's no Nobel Prize for cosmic inflation. There's no Nobel Prize for supersymmetry. What's the idea there?
Well, you know, in a sense, physics has from the beginning been an experimental science. When the modern quantum physics came, even the experiments were called theoretical physics because they were so new, in Sweden at least. It was from the beginning sort of a rule that it had to be really established, experimentally. And I think this reflects Alfred Nobel, who was an inventor. This is what he wanted. He was very keen on inventions and discoveries. So, this has been established from the beginning.
I wonder if it was special for you particularly, given your admiration for Nambu.
Well, it was a tricky thing. Let me not talk so much about Nambu. Let me talk more generally about spontaneous symmetry breaking, because this is one of those other miracles in physics. We know that the world really has a variety of phenomenon, and still, you can describe it with fairly simple equations. And spontaneous symmetry breaking is a way of letting the world flourish and still use fairly simple underlying theories. Of course, Nambu realized this and in a short letter laid the ground for all of nuclear physics. Before that he wrote a fantastic paper on superconductivity really explaining in depth the BCS theory. I should not say more. Anyone can read about the scientific background on the home page of the Nobel Foundation.
Lars, what about the decision to restrict the award to only three people, particularly in light of the fact that in modern physics with big science, collaborations often run into the dozens, if not the hundreds or the thousands?
Yeah, in the statutes it says it is limited to three. It doesn't say if this is three people, or three collaborations or anything. So, this was a rule from the beginning but was codified some 50 years ago, in writing. It is again a very difficult issue. The Nobel Foundation has not changed it, and it's not really discussed. I mean, this is what is in the statutes for the moment, and I cannot say anything more.
What has been so personally meaningful to you in serving on the Nobel committee?
I think that the most interesting thing is to learn so much, because one has to understand fields outside your own, which is very useful. So, that I liked a lot. Of course, you also learn to appreciate other subjects, which is always very useful. This is, how should I say it, it's very rewarding in that sense, to learn about other fields, to be forced somehow to learn about other fields.
What was your reaction, emotionally even, when the Higgs was discovered at the LHC?
Well, this is sort of outside any Nobel stuff. Of course, I was extremely pleased that it was found. Again, it was a fairly simple solution to a difficult problem. I remember Abdus Salam used to say back in the '70s that the world might be very poor in principles, but rich in particles. So, again, by having a new particle, you solved a lot of problems with the Higgs particle. It is a very strange particle, the way it fits into the Standard Model, and it might not be the final answer, how should I say? In a sense, I'm not sure, of course, but it really helps you to get consistent interactions with finite range. It is very interesting if you read the Yang-Mills paper. The story is that this idea was around, that perhaps you should be able to use non-Abelian gauge theories for strong interactions. It even goes back to my compatriot, Oscar Klein in 1938, but he didn't get it completely right. But he was onto it, and then Abdus Salam was certainly very interested in it. He had a student who wrote about it, and Pauli was thinking about it too, but he was very much against it because it gives a long-range force, and they were looking at the time to have short-range forces.
But Yang realized it, and if you're reading the paper very carefully, then in the end he has some sentences where he's arguing that there could very well be; he might not have said it like this, but it could very well be that there is a mechanism by which this force becomes short-range. I'm very impressed that he put that sentence in. Had it not been Frank Yang, had it just been someone who tried to impress people, they would have said it without deep thinking, but I'm sure that Yang thought about it deeply, and somehow, somewhere in the back of his mind, he could see that the theory was rich enough so that there was room for something like that. And sure enough, this is what the Higgs mechanism is. By very simple methods, you can get a short-range force with a consistent theory.
So, from the particle physics point of view, I was extremely happy when they found it. It could have been, of course, it could have been realized in different ways, in a more dynamical way without a particle. But then it would have been much more difficult to prove it. There is a completely fantastic paper by Sasha Polyakov and Sasha Migdal. They wrote it in 1964, when they were two 19-year-old undergraduates in Moscow. They wrote a paper where they use some dynamic symmetry breaking. This is a very complicated paper but correct and solved the problem of getting a short-range force. But since they were undergraduates, they were not allowed to publish it first. Eventually, a year after, it was published, mainly because Sasha Migdal's father was a famous academician, and he pushed it through. The Russian system was very strict and hierarchical. Sasha Polyakov, of course, all the time was hoping that they should not find a Higgs particle. So, he was disappointed. It's depending on what you hope for, so to speak. But my attitude is more like that of Abdus Salam, that we can have just more particles, no problem, as long as they solve the problems for us. So, for that reason I was very happy.
What new questions were able to be asked as a result of discovering the Higgs? What could the LHC do afterwards?
Well, what they can do is that they can measure very carefully all the couplings, and really check if they are consistent with the existing theory, or even more interesting, if they can find some kind of anomaly in it which would point to some new physics. So, that would be even more interesting. But now the other thing that LHC was essentially built for was to search for supersymmetry, and the people at CERN believed that it would come rather quickly after the Higgs, to find this supersymmetric particle. So, that's been a great disappointment.
Are you optimistic at all that in the upgrades at the LHC that supersymmetry may yet be seen?
I'm always optimistic. It might not be fair, but yeah. And in the end, you might see it indirectly. For example, you know, if you really study processes, you might see that things are missing. When people found the top quark, there had already been theoretical indications that there should be something. They had been able to pin down that there should be something in that region. So, perhaps, something similar can happen here, if it's not really discovered directly. So, that's why it's interesting with these anomalies in this g-2 experiment, or the CERN experiment. Properly interpreted, it might lead to that you see that there is a particle somewhere high up in energy perhaps that is affecting the whole thing. This is what one can hope for. So, I'm optimistic. I think supersymmetry is such a beautiful idea that I would be surprised if the world is not supersymmetric in the end.
What does math tell us that gives you the certainty or the belief that supersymmetry must be real?
Math, I don't know. I'm more naive. I think it's more of the mathematical beauty once you have supersymmetry. You get theories that are much better-behaved quantum mechanically because, go back to the zero-point fluctuations, the fermionic ones have opposite sign to the bosonic ones, and if they have the same mass, you can get them to cancel. You get much better convergence properties. And we know that we have bosons and fermions, and in a sense, why don't we have also bosonic coordinates and fermionic coordinates? It's a neat argument but really it is based on belief more than some heavy facts.
Lars, tell me about the impact on the work of Peter Freund for you.
Oh, Peter Freund. Well, it's not that he had much impact on me. I mean, Peter Freund was a good friend of mine. He wrote some interesting papers, mainly the ones in the beginning of the '80s in supergravity where we were sort of rather close. There's the paper by Freund-Rubin. He was of course a very clever person, but he was not one of those who was somehow pushing a field. He was finding interesting facts in various fields. I guess he was an important person in the Chicago group, but he didn't have much influence on me scientifically, I should say. He was the chairman of the Erwin Schrödinger Foundation and I gave the Erwin Schrödinger lecture in 2010, I think it was. He came from a rich East-European culture and it was always interesting to discuss with him.
Lars, would you say in the past 10 years, supergravity has remained a rich field?
Well, in one sense it's richer because people find more and more solutions. Now you see also very computationally advanced techniques to find higher order corrections. If you think about supergravity, and if you just want to treat it as a perturbative quantum field theory, say, and you do this for the N=8 theory the way it was first written down, you expand in terms of the gravity field, and in terms of Newton's coupling constant. Then you get to the 4-point coupling. It turns out that if you write it out, all the 4-point couplings, there are about 5,000 terms in it, which means that of course it's impossible to use that formula as such. And then you might think that these 5,000 terms are fairly random in a sense, in their coupling strength, so to speak. It's then stupid to believe that there should be some simplicity, and you will have so many strange effects at that order, and it would be just a complete mess.
But if you take the N=8 supergravity and you take the 4 gravitons scattering, and you compute the first order you get what's essentially Newton's term, and then you go to the next one-loop correction. It turns out to be the simplest one you can have in a quantum field theory. It's the same with N=4 Yang-Mills. It just passes all the tests you can ask for a consistent theory, and nothing more. Any other gravity theory, or Yang-Mills theory, has a more complicated set of terms for the S-matrix. And this goes on. So, you'll be able to say that maximal supergravity theory is in a sense the simplest quantum gravity theory that you can write down. And in order to write it down, you have to use this enormously complicated machinery, etc. This is what's so fascinating, that it somehow tells you that this is the bare bone of quantum gravity. It's the same for N=4 Yang-Mills. It's the simplest quantum field theory in 4 dimensions perturbatively, just passing all the tests you can ask for theoretically. But then you go to Maldacena's result, and you find that if you take N=4 Yang-Mills and look at the non-perturbative sector of it, then you realize that it knows about string theory.
There is another aspect I should mention. You take a scattering amplitude in N=8 supergravity, and you find that that's essentially just, in a certain sense, the square of the N=4 one. So, you can say that the N=4 is the basic theory. You can use it to write the perturbative, the small coupling expansion of the N=8 supergravity. Thus, in a sense N=4 is from that point of view sort of the starting point of all this, then on the other hand, if we look at the weak coupling limit of N=4 from another perspective, it gives you insight into the strong coupling regime of supergravity, the Superstring Theory. It gives you information about all those things. I cannot get around this. There is this beautiful package, everything you know is essentially in the N=4 theory. And then you might ask how is this related to Nature? Well, in that sense, these are hypothetical models.
As I said, these are the simplest bare bone theories; these are the starting points. Now we can start to ask, how much can you shift a little bit here and a little bit there and still have a consistent theory? I think this will be one way of getting to a true unified theory. Of course, it's impossible to do it, but it's a logical way of doing it. You loosen up because it doesn't need to be a finite theory. It's enough to be renormalizable. And then you can perhaps get the correct description of the world that way. So, from that point, both N=4 and N=8 supergravity, and also going down to lower supersymmetry, they are so important in the basic understanding of relativistic many-body theories in 4 dimensions. And somehow, they should also then be able to lead us into the correct theory.
The question is, suppose one had found what is the correct theory that describes the basic physics in 4 dimensions. Would that be a unique theory, or is it one out of 10500 or so, which Lenny Susskind and other people are saying. That could very well be true. That's another way of thinking, but suppose there was just a unique way of pushing it, and you get a unique theory. If there was just a unique theory that would satisfy all the constraints you could put on the physical theory, that would somehow be an explanation for why physics works, why the world works like it works. Perhaps it's too optimistic; it's a bit naïve, but that would be a logic possibility and a very beautiful way of understanding the world.
Lars, you may have heard John Schwarz say, "String theory is smarter than we are."
Absolutely, and I think, sure. Even N=4 is smarter, it might be even smarter than the Superstring. Absolutely. I think, in a sense we have been very lucky to be able to find these theories and be able to work on them for so many years, and find all these miracles in them, and still we've probably only scratched the surface. So, this comes back to what I was saying that we've only really investigated a very small part of those theories.
Lars, even though these fields have not been borne out experimentally, I wonder if you can reflect on the value of this work more generally in astrophysics, and in cosmology.
I'm not sure too much about that, to be honest. One big issue has been whether one can understand better black hole physics this way. But no, I think I should pass. I don't have too much to say about that.
What about quantum information?
I think it's the same thing there. I think quantum information is at a rather early stage these days, and this is wonderful for them. It's like we were 50 years ago in dual model, string theory, where you could very easily write a paper. As I said, Holger Bech and I wrote a paper in three days, and it became quite a famous paper in certain circles. So, it's a very good question that you ask, because you see, according to the logic that I'm bringing forward, I think all these things somehow should get together one day. There ought to be connections also into that field, but I know too little about it. But I'm sure someday one smart guy will find something that can connect them.
Lars, what are you most proud of with regard to the coordination of the Superstring Theory Network for the EU?
I'm not sure I'm so proud of that. That was funny. It was a way of keeping the groups together and collaborating and having a chance to compete with the American groups somehow. There were at the time three big networks, and ours was more loosely connected. There was one well connected, really, first in Leuven in Belgium that then moved over to Munich as the coordinating group, and one in Paris. The networks were very useful. What I'm most proud of is that this was a way of getting the European graduate students to get together to learn from each other. We tried to have schemes by which they could visit the various groups, because European groups are mostly small and either in clusters or very scattered. It's like in the US—If you're in New York, you have several universities around. You can sit in New York, and you go to Princeton, and you can go to Rutgers, and then you have all the universities within the city, so you could go to seminars every day if you want. But if you're out in University of Oklahoma or someplace like that, then you are, I guess, much more isolated.
In Europe, you can be even more isolated also due to tradition, and usually the groups were smaller. For this reason, it was very helpful. And then we had the Eastern European problem; there were groups in Eastern Europe that had been completely isolated. They were really struggling, so somehow, we managed to get them through. I'll give you a story. It was in the beginning of the 1990s, I was the chairman of the board of Nordita, the institute in Copenhagen, and in 1991 just before the Soviet Union broke down. I had the idea that we should try to involve the Baltic states, Estonia, Latvia, and Lithuania into the Nordic community somehow. Historically, they had been rather close, but then during the Soviet times, we knew nothing about them. They are neighbors to Sweden. Well, there is water in between, but in principle, in old times there were good connections.
So, I went on a tour in the late winter of '91. I first came to Estonia, and I found that actually there were probably two groups doing physics. In Latvia, there was one university. There were about 7 theoretical physicists in the whole country. It was a country of 1 or 2 million people. Lithuania was a little bit different. They used to be called the capital of Clebsch-Gordan coefficients. They had been doing Clebsch-Gordan coefficients for many years. They were atomic physicists. But you know, they were completely isolated. So, we tried in our network to have connections with groups like those, tried to invite and get them interested in modern physics. But also in Southeast Europe, we tried to get those people to be engaged. Of course, in the end, what that led to is that indeed the really good students from Southeast Europe went to United States. It was a huge brain drain instead there, but one can always hope that they can come back. So, the networks had this mission, I would say, of unifying and helping, and I think it worked. Then they changed the rules, and we were somehow not given any further money. That was in 2008. Other field had complained that Superstring theory got too much funding.
Lars, you say that you're an optimist, so for the last part of our talk, let's look to the future and think about things to be optimistic about in physics. What is most exciting to you personally that you might be around to see, and what are the things where, even longer term than that, as you say 100 years into the future, what might you imagine can be understood then that right now we have only an elemental understanding, just scratching the surface?
This is essentially what I've been talking about. What I really hope for in the near future is that we will find something beyond the Standard Model. Hopefully supersymmetry and also dark matter. Hopefully it's the same, but it need not be the same, of course. And there, I'm really optimistic because we know that there is dark matter, and there are some beautiful experiments around the world, both accelerator-based and non-accelerator-based experiments. The Chinese have this marvelous tunnel into a big mountain with 2,400 meters of mountain above it, and they can drive into it with big trucks where they're setting up experiments. So, I think that they will be able to find dark matter. So, that would be exciting, and that would help us much to understand further the Standard Model. But then, of course, in the long run, as I said, my dream is that one can really one day formulate the fundamental laws of physics in terms of a model or framework or something, by which one can in principle compute what's happening in particle physics, condensed matter and the macroscopic world. In the end we won't do it, because it probably won't be necessary.
It probably will not be interesting to do the calculations, but it will be philosophically very rewarding to know that there is this kind of framework. What I would hate to see is that it would be that we will somehow give up, saying it's just more and more complicated, so it's meaningless to search more for the truth deeper down. This is the attitude for the moment, because everything should be very entrepreneurial; you should use new physics for constructing new gadgets. I am disappointed that we don’t spend much more efforts to understand the basic laws of our universe, to understand in a logical way why we are here. So, from that point of view, this is the way I hope fundamental physics will go 100 years from now.
Lars, it's been a great pleasure spending this time with you. I'm so happy we were able to do this and capture all of your memories and perspectives for our collection. So, thank you so much. I really appreciate it.