Conformal Bootstrap with Reinforcement Learning

TL;DR

This paper introduces reinforcement learning techniques, specifically soft Actor-Critic algorithms, to efficiently explore the conformal bootstrap space, enabling high-dimensional searches for conformal field theory data from a single crossing equation.

Contribution

The paper presents a novel application of RL algorithms to conformal bootstrap, achieving high-dimensional searches in CFT parameter space with minimal input and demonstrating effectiveness on well-known 2D models.

Findings

Successful high-dimensional searches up to 36 dimensions.

Efficient exploration of CFT data using RL with minimal input.

Applicable to higher-dimensional CFTs beyond 2D models.

Abstract

We introduce the use of reinforcement-learning (RL) techniques to the conformal-bootstrap programme. We demonstrate that suitable soft Actor-Critic RL algorithms can perform efficient, relatively cheap high-dimensional searches in the space of scaling dimensions and OPE-squared coefficients that produce sensible results for tens of CFT data from a single crossing equation. In this paper we test this approach in well-known 2D CFTs, with particular focus on the Ising and tri-critical Ising models and the free compactified boson CFT. We present results of as high as 36-dimensional searches, whose sole input is the expected number of operators per spin in a truncation of the conformal-block decomposition of the crossing equations. Our study of 2D CFTs uses only the global $so(2,2)$ part of the conformal algebra, and our methods are equally applicable to higher-dimensional CFTs. When combined with other, already available, numerical and analytical methods, we expect our approach to yield an exciting new window into the non-perturbative structure of arbitrary (unitary or non-unitary) CFTs.