Deep learning and the AdS/CFT correspondence

作     者：Koji Hashimoto Sotaro Sugishita Akinori Tanaka Akio Tomiya 

作者机构：Department of Physics Osaka University Toyonaka Osaka 560-0043 Japan Mathematical Science Team RIKEN Center for Advanced Intelligence Project (AIP)1-4-1 Nihonbashi Chuo-ku Tokyo 103-0027 Japan Department of Mathematics Faculty of Science and Technology Keio University 3-14-1 Hiyoshi Kouhoku-ku Yokohama 223-8522 Japan Interdisciplinary Theoretical & Mathematical Sciences Program (iTHEMS) RIKEN 2-1 Hirosawa Wako Saitama 351-0198 Japan Key Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics Central China Normal University Wuhan 430079 China 

出 版 物：《Physical Review D》 (Phy. Rev. D)

年 卷 期：2018年第98卷第4期

页      面：046019-046019页

核心收录：

基　　金：RIKEN Japan Society for the Promotion of Science, JSPS, (JP15K13483, JP15H03658, JP17H06462, 16J01004) Japan Society for the Promotion of Science, JSPS National Natural Science Foundation of China, NSFC, (11535012) National Natural Science Foundation of China, NSFC Fundação para a Ciência e a Tecnologia, FCT, (PTDC/CCI-BIO/29266/2017) Fundação para a Ciência e a Tecnologia, FCT 

主　　题：Gauge-gravity dualities Machine learning 

摘      要：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 ϕ4 theory with unknown mass and coupling, in unknown curved spacetime with a black hole horizon, we demonstrate that our deep learning (DL) framework can determine the systems that fit given response data. First, we show that, from boundary data generated by the anti–de Sitter (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 the magnetic response of the strongly correlated material Sm0.6Sr0.4MnO3. This AdS/DL correspondence not only enables gravitational modeling of strongly correlated systems, but also sheds light on a hidden mechanism of the emerging space in both AdS and DL.