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.
Highlights
The nonperturbative formulation of a generic quantum field theory (QFT) and the analytic, or numerical, solution of its dynamics remains an extremely challenging conceptual and computational problem with important theoretical and experimental implications.The problem becomes more tractable in conformal field theories (CFTs): a special class of QFTs that describe typically the short and large-distance behaviors of generic QFTs
We demonstrate that suitable soft Actor-Critic RL algorithms can perform efficient, relatively cheap highdimensional searches in the space of scaling dimensions and operator product expansion (OPE)-squared coefficients that produce sensible results for tens of CFT data from a single crossing equation
In this paper we introduced the use of reinforcementlearning techniques into the conformal bootstrap program
Summary
The nonperturbative formulation of a generic quantum field theory (QFT) and the analytic, or numerical, solution of its dynamics remains an extremely challenging conceptual and computational problem with important theoretical and experimental implications. The problem becomes more tractable in conformal field theories (CFTs): a special class of QFTs that describe typically the short and large-distance behaviors of generic QFTs. Most notably, in a unitary, relativistic CFT in D spacetime dimensions, the local structure of the theory is characterized by a set of discrete data: the scaling dimensions Δi of local conformal primary operators Oi and their operator product expansion (OPE) coefficients Ckij. In a unitary, relativistic CFT in D spacetime dimensions, the local structure of the theory is characterized by a set of discrete data: the scaling dimensions Δi of local conformal primary operators Oi and their operator product expansion (OPE) coefficients Ckij Once these data are known, the generic correlation function of any local operator in the theory can be determined.
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