Vyacheslav "Slava" Rychkov (Вячеслав Рычков)
Permanent professor of theoretical physics, Institut des Hautes Études Scientifiques
What's new:
10/09/2025 Fradkin and Palchik's dreams about CFT in \(d>2\) dimensions
A few days ago, a colleague sent me an email asking why my recent article about the conformal bootstrap history did not mention Fradkin and Palchik. The email included a supporting opinion by... ChatGPT! Normally I would not respond to a machine. However, the question prompts me to tell a story. Spoiler: no need to update the article so far.
In 1996, Fradkin and Palchik published a thick book about Conformal Field Theory in general number of spacetime dimensions, accompanied by a review in Physics Reports. There, they make a surprising claim that the null states of 2D CFT allow generalization to higher dimensions. If true, this would be spectacular, as it could lead to an exact solution of CFTs in \(d>2\) such as the 3D Ising CFT. In 2016, Liam Fitzpatrick and myself did a fair amount of calculations trying to verify this claim, but we did not succeed. It may be wrong (my best bet) or it may be that we just did not get it. Others are welcome to give it a try. But in the meantime, Fradkin and Palchik's work remains in the limbo.
Here's some macabre humour. With Liam, we called their book "The book of the dead". (By that time, Fradkin passed away, while Palchik quit physics to lead a consulting center based on a quantum approach to psychology.) Furthermore, we called "Egyptian operator" the operator which was supposed to make vanish a three-point function, as a consequence of a \(d\)-dimensional null state condition. Unfortunately in our checks this vanishing did not happen, except for \(d=2\).
4/09/2025 A new Simons collaboration
Simons Foundation has recently announced support for the new Simons Collaboration on Probabilistic Paths to Quantum Field Theory. I am excited about this new scientific endeavor, which I joined as one of 14 Principal Investigators, along with Roland Bauerschmidt, Denis Bernard, Sourav Chatterjee, Massimiliano Gubinelli, Colin Guillarmou, Martin Hairer, Nina Holden, Antti Kupiainen, Nikita Nekrasov, Remi Rhodes, Fredrik Viklund, Yilin Wang, and Scott Scheffield (Director).
4/09/2025 Conformal bootstrap: from Polyakov to our times
This new paper traces the history of the conformal bootstrap, starting with the fateful 1970 meeting of Hans Kastrup, Alexander Polyakov and Alexander Migdal at the XV ICHEP conference in Kyiv. I also recount the story of my own numerical bootstrap collaborations, and throw in a section on some selected open problems. I conclude by emphasizing experimental evidence of manifestations of conformal symmetry in nature. Of course, more experimental evidence is always welcome. I am currently pursuing some ideas in this direction.
29/07/2025 Bootstrapping with samba
I am attending the Bootstrap 2025 program at the Instituto Principia in São Paulo, Brazil, where Fabiana De Cesare spoke today about our recent work "Disturbing news about the \(2+\epsilon\) expansion". I invite you to watch her excellent talk. The \(2+\epsilon\) expansion of the \(O(N)\) nonlinear sigma model is a classic subject going back to the work of Polyakov, Brézin, and Zinn-Justin in the 1970's. Most people believe that if properly done it should give the same critical exponents in \(d=3\) as the \(4-\epsilon\) expansion of Wilson and Fisher. However as our work explains, this is unlikely to be true, at least if one uses the standard textbook implementation. This expansion may instead describe some other family of theories. An interesting open problem is how to modify the \(2+\epsilon\) expansion so that this problem is resolved. Future work will hopefully clarify the situation.
10/07/2025 Say no to Google
Time to stop relying on Google. I moved from gmail to protonmail. I also moved my personal website from google sites to the IHES domain, editable through a CNRS hosting platform.
03/06/2025 Tensor Renormalization Group Meets Computer Assistance
This new paper marks the next crucial step in the program of studying 2D lattice models with the help of tensor network RG, which I am pursuing with Tom Kennedy and my PhD student Nikolay Ebel. We usher in the "hat-tensor", a finite-dimensional bounding box in which an infinite-dimensional tensor lives. A computable "master function" governs evolution of the hat-tensor from one RG step to the next. In this work we demonstrate the utility of these tools near the high-T fixed point. In the future, they will be instrumental when constructing the critical fixed point - a final goal of this long-term project.