2023 ICTP Prize

Every year ICTP awards the ICTP Prize to scientists from developing countries to recognize their outstanding and original contributions to physics. The 2023 ICTP Prize winners are Mohit Kumar Jolly from India and Xinan Zhou from China. Both of them were in Trieste to attend the ICTP Prize Ceremony that took place on Wednesday 28 August, when they also agreed to answer a few questions about their work and about the Prize.

Xinan Zhou of the Kavli Institute for Theoretical Sciences (KITS), University of Chinese Academy of Sciences (UCAS), Beijing, and ShanghaiTech University, received the ICTP Prize for his contributions leading to new techniques to compute correlation functions in conformal field theories in the context of the AdS/CFT correspondence, and for developing new approaches to the analytic conformal bootstrap. In this interview, he explains what this means, and tells us how he ended up working on conformal field theories as a young PhD student looking for an exciting problem to solve.

How would you summarize the contributions that earned you the ICTP Prize to someone who is not in your field?

These works are about the so-called conformal field theories (CFTs), which are a set of theories describing a variety of physical phenomena including second order phase transitions – such as the one that takes place when water boils. In general, they are very difficult to study analytically because they are non-perturbative. This means that interactions are strong and cannot be handled by treating them as small perturbations to non-interacting systems. An important breakthrough to understanding CFTs was made by Juan Maldacena and goes by the name of the anti de Sitter/conformal field theory (AdS/CFT) correspondence. It establishes an exact correspondence between   certain CFTs and some gravity theories in a curved higher-dimensional spacetime. The latter are easier to study because, according to this correspondence, we only need to consider the perturbative regime, where we can study such theories analytically. However, in practice, this remains extremely difficult. My main contribution was to develop efficient techniques to better harness the computational power of the AdS/CFT correspondence.

Another modern approach to CFTs is the so-called conformal  bootstrap, which revived old ideas from the 1960s and ‘70s and aims to solve CFTs using only general constraints imposed by the general principles of CFTs. My work in that direction tried to understand how to extract constraints from CFTs in a systematic way which can be studied analytically.

What new mathematical and computational methods have you developed along the way?

In CFTs, the most basic observables are correlation functions, which measure the correlation of fluctuations at different points in spacetime. Thanks to the AdS/CFT correspondence, the problem of calculating these complex correlations can be reduced to  that of computing scattering amplitudes in the curved AdS space, and that can be done using diagrams. These diagrams are called Feynman diagrams in flat space, and Witten diagrams in AdS. Again, this prescription works in principle but is extremely complicated in practice because of the infinitely many particles that one encounters due to the presence of an internal space.  The interactions of these infinitely many particles are so complicated that they would take more than a dozen pages to write down, even in the simplest model where the AdS space is five dimensional. Inspired by the idea behind bootstrap, I developed a new method. It turns out that thanks to symmetries and consistency conditions, one can fix these correlators by reformulating the task as finding the solution to an algebraic problem. For this simplest model, it is possible to use this method to obtain all infinitely many four-point correlators, bypassing all the complicated intermediate steps and without even computing a single Witten diagram.

Witten diagrams remain, however, extremely useful because of their very interesting mathematical properties, which help us understand the structure of constraints in general CFTs. More precisely, they give rise to a new basis to decompose correlators, in which we can systematically extract analytically all the constraints that are imposed by the basic principles of CFTs.

What drew you to working on conformal field theory and the AdS/CFT correspondence?

I would say that it is largely thanks to my PhD advisor, Leonardo Rastelli, that I started working on this field.  In fact, the very first problem I set out to solve in my PhD was about some algebraic structures in superconformal field theories. But it didn’t quite work out for various reasons, partially also because it felt a bit too mathematical to  me. Then Leonardo suggested that I work on this new problem of computing holographic correlators, which in retrospect is much more difficult and is something that he himself worked on when he was a graduate student with his then advisor Daniel Freedman. I liked this problem a lot better because it is something which I could experiment and use my intuition with. Perhaps we can call it experimental theoretical physics. When I started looking into it, people had already been working on it for almost 20 years, and there had been several technical developments since then, making it conceivable that one could push the computation a bit further and calculate more examples. But I managed to find a way to solve the problem in general using a very different method. Many things opened up and  what previously seemed impossible suddenly became possible because of this work. Later it also intersected with many other interesting problems and that’s why I kept working on CFTs and AdS/CFT. So I’m very grateful to Leonardo for suggesting this problem.

If you had a magical stick, what problem in physics would you like to solve?

The first thing I would ask for, if I was given a magical stick, would be more magical sticks, because there are so many problems that I would like to solve! But if I had to choose, the first thing that I would like to solve is the problem of strong coupling, for which the standard techniques in Quantum Field Theory textbooks fail. The phenomenon of strong coupling, however, is everywhere in physics, from the critical point of water to the confinement of quarks. Significant progress has been made, for example, through the numerical conformal bootstrap, which gives very precise estimates of the critical exponents, but it would be very interesting to be able to look under the hood and have an analytic understanding for why these numbers are these numbers. Another problem I’d like to understand is turbulence in fluid mechanics, which is a very difficult problem in classical physics.

What does the ICTP Prize mean to you?

It means a lot. It’s a great honor for me to receive this highly distinguished prize from ICTP.

It certainly feels great that my contributions to the field are getting recognized and I think such recognitions are especially important for people who are in their early careers. At the same time,   it also stimulates me to work harder and it is a great encouragement for me to challenge bigger problems in my future career.