Solving Conformal Field Theories with Artificial Intelligence

TL;DR

This paper introduces the use of Reinforcement Learning, specifically the soft Actor-Critic algorithm, to numerically solve conformal field theories by efficiently navigating the crossing equations, including well-known models.

Contribution

It pioneers the application of Reinforcement Learning to the conformal bootstrap, enabling high-dimensional searches for diverse CFTs across dimensions.

Findings

Successfully identified 2D Ising model and compactified scalar CFTs

Demonstrated efficient high-dimensional search capabilities

Extended methods to both unitary and non-unitary CFTs

Abstract

In this paper we deploy for the first time Reinforcement-Learning algorithms in the context of the conformal-bootstrap programme to obtain numerical solutions of conformal field theories (CFTs). As an illustration, we use a soft Actor-Critic algorithm and find approximate solutions to the truncated crossing equations of two-dimensional CFTs, successfully identifying well-known theories like the 2D Ising model and the 2D CFT of a compactified scalar. Our methods can perform efficient high-dimensional searches that can be used to study arbitrary (unitary or non-unitary) CFTs in any spacetime dimension.