Machine Learning Holographic Mapping by Neural Network Renormalization Group

Abstract

The exact holographic mapping (EHM) provides an explicit duality map between a conformal field theory (CFT) configuration and a massive field propagating on an emergent classical geometry. However, designing the optimal holographic mapping is challenging. Here we introduce the neural network renormalization group as a universal approach to design generic EHM for interacting field theories. Given a field theory action, we train a flow-based hierarchical deep generative neural network to reproduce the boundary field ensemble from uncorrelated bulk field fluctuations. In this way, the neural network develops the optimal renormalization group transformations. Using the machine-designed EHM to map the CFT back to a bulk effective action, we determine the bulk geodesic distance from the residual mutual information. We apply this approach to the complex ${\varphi }^4$ theory in two-dimensional Euclidian spacetime in its critical phase, and show that the emergent bulk geometry matches the three-dimensional hyperbolic geometry.

9 pages, 7 figures + appendix

References in corpus (15)

• Learning phase transitions by confusion
• Identifying topological order through unsupervised machine learning
• Self-Learning Monte Carlo Method
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Machine learning vortices at the Kosterlitz-Thouless transition
• Regressive and generative neural networks for scalar field theory
• Deep Learning and Holographic QCD
• Super-resolving the Ising model with convolutional neural networks
• AdS/CFT as a deep Boltzmann machine
• Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows
• Holography as deep learning
• Gradient flow and the renormalization group
• Restricted Boltzmann Machines for the Long Range Ising Models
• Self-learning Monte Carlo method with Behler-Parrinello neural networks
• Optimal Renormalization Group Transformation from Information Theory

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