Solving Conformal Field Theories with Artificial Intelligence

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.

arXiv comment6 pages; v2: references added

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Cited by in corpus (19)

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• Spectrum continuity and level repulsion: the Ising CFT from infinitesimal to finite $\mathbf{\epsilon }$
• 6D (2,0) Bootstrap with soft-Actor-Critic
• Improving the five-point bootstrap
• Ising model close to $d=2$
• Easy bootstrap for the 3D Ising model: a hybrid approach of the lightcone bootstrap and error minimization methods
• Conformal Fields from Neural Networks
• Conformal Bootstrap Deformations
• Anomalous dimensions of partially-conserved higher-spin currents from conformal field theory: bosonic ${\varphi }^{2n}$ theories
• Constructing and Machine Learning Calabi-Yau Five-folds
• Black holes and the loss landscape in machine learning
• Conformal Bootstrap with Reinforcement Learning
• Calabi-Yau Four/Five/Six-folds as ${\mathbb{P}}_{\text{w}}^n$ Hypersurfaces: Machine Learning, Approximation, and Generation
• Accurate boundary bootstrap for the three-dimensional O($N$) normal universality class
• Anomalous dimensions from conformal field theory: Generalized ${\varphi }^{2n+1}$ theories
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories
• Topological Learning in Multi-Class Data Sets
• Boundary anomalous dimensions from BCFT: O($N$)-symmetric ${\varphi }^{2n}$ theories with a boundary and higher-derivative generalizations
• A Monte Carlo approach to the conformal bootstrap