Abstract
In this Letter, we deploy for the first time reinforcement-learning algorithms in the context of the conformal-bootstrap program 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 nonunitary) CFTs in any spacetime dimension.
Highlights
In this Letter, we deploy for the first time reinforcement-learning algorithms in the context of the conformal-bootstrap program to obtain numerical solutions of conformal field theories (CFTs)
Introduction.—The generic short- and large-distance behavior of a quantum field theory is described by a conformal field theory (CFT)
CFTs appear in numerous physical applications, e.g., describing the physics of continuous phase transitions, and in many modern theoretical explorations of the nonperturbative structure of quantum field theories
Summary
In modern reincarnations of the conformal bootstrap, starting with the seminal work of [3], one turns the problem around: Instead of searching directly for exact or approximate solutions to the crossing equations, one makes a minimal assumption about the spectrum of a unitary CFT and asks whether the crossing equations can be satisfied; if not, the assumption can be eliminated In recent years, this approach has been implemented with great success in a variety of contexts—see, e.g., [4,5,6] for reviews—yielding. Its basic modus operandi involves selecting ad hoc assumptions for a handful of free parameters, while the resulting constraints on the CFT data favor the study of special CFTs on the boundary of the allowed and disallowed regions, making it harder to study particular classes of generic theories (e.g., one’s favorite gauge conformal field theory) This standard approach suffers from exponential scaling on the dimensionality of the search space, which constitutes a major obstruction.
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