Deep Learning and AdS/CFT

TL;DR

This paper introduces a deep neural network framework that models the AdS/CFT correspondence, enabling the extraction of bulk spacetime metrics and physical parameters from boundary data of strongly correlated systems.

Contribution

It presents a novel deep learning approach to holography, allowing data-driven modeling of bulk geometry and physical parameters in AdS/CFT without prior knowledge.

Findings

Successfully reproduces bulk metric from boundary data.

Determines bulk parameters like mass and coupling from experimental data.

Demonstrates applicability to real strongly correlated material data.

Abstract

We present a deep neural network representation of the AdS/CFT correspondence, and demonstrate the emergence of the bulk metric function via the learning process for given data sets of response in boundary quantum field theories. The emergent radial direction of the bulk is identified with the depth of the layers, and the network itself is interpreted as a bulk geometry. Our network provides a data-driven holographic modeling of strongly coupled systems. With a scalar $\phi^4$ theory with unknown mass and coupling, in unknown curved spacetime with a black hole horizon, we demonstrate our deep learning (DL) framework can determine them which fit given response data. First, we show that, from boundary data generated by the AdS Schwarzschild spacetime, our network can reproduce the metric. Second, we demonstrate that our network with experimental data as an input can determine the bulk metric, the mass and the quadratic coupling of the holographic model. As an example we use the experimental data of magnetic response of a strongly correlated material Sm$_{0.6}$Sr$_{0.4}$MnO$_3$. This AdS/DL correspondence not only enables gravity modeling of strongly correlated systems, but also sheds light on a hidden mechanism of the emerging space in both AdS and DL.