Machine Learning Etudes in Conformal Field Theories

Abstract

We demonstrate that various aspects of Conformal Field Theory are amenable to machine learning. Relatively modest feed-forward neural networks are able to distinguish between scale and conformal invariance of a three-point function and identify a crossing-symmetric four-point function to nearly a hundred percent accuracy. Furthermore, neural networks are also able to identify conformal blocks appearing in a putative CFT four-point function and predict the values of the corresponding OPE coefficients. Neural networks also successfully classify primary operators by their quantum numbers under discrete symmetries in the CFT from examining OPE data. We also demonstrate that neural networks are able to learn the available OPE data for scalar correlation function in the 3d Ising model and predict the twists of higher-spin operators that appear in scalar OPE channels by regression.

arXiv comment29 pages, 24 figures, references updated

References in corpus (19)

• DGM: A deep learning algorithm for solving partial differential equations
• Machine learning phases of matter
• AdS Dual of the Critical O(N) Vector Model
• Solving the 3D Ising Model with the Conformal Bootstrap
• Massless Higher Spins and Holography
• Precision Islands in the Ising and $O(N)$ Models
• The Analytic Bootstrap and AdS Superhorizon Locality
• An AdS_3 Dual for Minimal Model CFTs
• Chern-Simons Theory with Vector Fermion Matter
• Machine learning quantum phases of matter beyond the fermion sign problem
• Large Spin Perturbation Theory
• A Mellin space approach to the conformal bootstrap
• Solving differential equations with neural networks: Applications to the calculation of cosmological phase transitions
• Machine Learning of Calabi-Yau Volumes
• Diagonal Limit for Conformal Blocks in d Dimensions
• Deep Learning and AdS/CFT
• Scalar CFTs and Their Large N Limits
• Learning the Ising Model with Generative Neural Networks
• On the Holography of Free Yang-Mills

Cited by in corpus (6)

• The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning
• Machine learning for complete intersection Calabi-Yau manifolds: a methodological study
• Machine Learning Lie Structures & Applications to Physics
• Graph Laplacians, Riemannian Manifolds and their Machine-Learning
• Universes as Big Data
• Conformal Bootstrap with Reinforcement Learning