Conformal Bootstrap with Reinforcement Learning
arXiv:2108.09330 · doi:10.1103/PhysRevD.105.025018
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 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.
arXiv comment54 pages; v2: typos corrected and references added; v3: minor corrections
References in corpus (30)
- Continuous control with deep reinforcement learning
- Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor
- Bounding scalar operator dimensions in 4D CFT
- New Developments in FeynCalc 9.0
- The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
- Solving the 3D Ising Model with the Conformal Bootstrap
- FeynCalc 9.3: New features and improvements
- Bootstrapping Mixed Correlators in the 3D Ising Model
- OPE Convergence in Conformal Field Theory
- Bounds on 4D Conformal and Superconformal Field Theories
- Bootstrapping Conformal Field Theories with the Extremal Functional Method
- More constraining conformal bootstrap
- Boundary and Interface CFTs from the Conformal Bootstrap
- Critical exponents of the 3d Ising and related models from Conformal Bootstrap
- Virasoro conformal blocks in closed form
- Conformal Blocks for Arbitrary Spins in Two Dimensions
- Branes with Brains: Exploring String Vacua with Deep Reinforcement Learning
- Closure of the Operator Product Expansion in the Non-Unitary Bootstrap
- Truncatable bootstrap equations in algebraic form and critical surface exponents
- Fast Conformal Bootstrap and Constraints on 3d Gravity
- Navigator Function for the Conformal Bootstrap
- Solving Conformal Field Theories with Artificial Intelligence
- Scaling the semidefinite program solver SDPB
- Conformal bootstrap for percolation and polymers
- Conformal Bootstrap Analysis for Yang-Lee Edge Singularity
- Extremal bootstrapping: go with the flow
- New method for the conformal bootstrap with OPE truncations
- Conformal Bootstrap Analysis for Single and Branched Polymers
- Machine Learning Etudes in Conformal Field Theories
- Adversarially Guided Actor-Critic