Machine Learning Holographic Mapping by Neural Network Renormalization Group
Hong-Ye Hu, Shuo-Hui Li, Lei Wang, Yi-Zhuang You
Received Date: 14th December 19
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 that flows to CFT, 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 $\phi^4$ theory in two-dimensional Euclidian spacetime in its critical phase, and show that the emergent bulk geometry matches the three-dimensional hyperbolic geometry.
Read in full at arXiv.
This is an abstract of a preprint hosted on an independent third party site. It has not been peer reviewed but is currently under consideration at Nature Communications.