2018年2月22日
Deep Learning and AdS/CFT
Phys. Rev. D 98, 046019 (2018)
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- 記述言語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1103/PhysRevD.98.046019
We present a deep neural network representation of the AdS/CFT<br />
correspondence, and demonstrate the emergence of the bulk metric function via<br />
the learning process for given data sets of response in boundary quantum field<br />
theories. The emergent radial direction of the bulk is identified with the<br />
depth of the layers, and the network itself is interpreted as a bulk geometry.<br />
Our network provides a data-driven holographic modeling of strongly coupled<br />
systems. With a scalar $\phi^4$ theory with unknown mass and coupling, in<br />
unknown curved spacetime with a black hole horizon, we demonstrate our deep<br />
learning (DL) framework can determine them which fit given response data.<br />
First, we show that, from boundary data generated by the AdS Schwarzschild<br />
spacetime, our network can reproduce the metric. Second, we demonstrate that<br />
our network with experimental data as an input can determine the bulk metric,<br />
the mass and the quadratic coupling of the holographic model. As an example we<br />
use the experimental data of magnetic response of a strongly correlated<br />
material Sm$_{0.6}$Sr$_{0.4}$MnO$_3$. This AdS/DL correspondence not only<br />
enables gravity modeling of strongly correlated systems, but also sheds light<br />
on a hidden mechanism of the emerging space in both AdS and DL.
correspondence, and demonstrate the emergence of the bulk metric function via<br />
the learning process for given data sets of response in boundary quantum field<br />
theories. The emergent radial direction of the bulk is identified with the<br />
depth of the layers, and the network itself is interpreted as a bulk geometry.<br />
Our network provides a data-driven holographic modeling of strongly coupled<br />
systems. With a scalar $\phi^4$ theory with unknown mass and coupling, in<br />
unknown curved spacetime with a black hole horizon, we demonstrate our deep<br />
learning (DL) framework can determine them which fit given response data.<br />
First, we show that, from boundary data generated by the AdS Schwarzschild<br />
spacetime, our network can reproduce the metric. Second, we demonstrate that<br />
our network with experimental data as an input can determine the bulk metric,<br />
the mass and the quadratic coupling of the holographic model. As an example we<br />
use the experimental data of magnetic response of a strongly correlated<br />
material Sm$_{0.6}$Sr$_{0.4}$MnO$_3$. This AdS/DL correspondence not only<br />
enables gravity modeling of strongly correlated systems, but also sheds light<br />
on a hidden mechanism of the emerging space in both AdS and DL.
- リンク情報
- ID情報
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- DOI : 10.1103/PhysRevD.98.046019
- arXiv ID : arXiv:1802.08313