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arXiv 1802.08313hep-th
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深度学习和AdS/CFT

Deep Learning and AdS/CFT

Koji Hashimoto, Sotaro Sugishita, Akinori Tanaka, Akio Tomiya

备注：
7 pages, 6 figures; Supplemental material: 8 pages, 5 figures
发表信息：
Phys. Rev. D 98, 046019 (2018)
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摘要：

我们提出了一个深度神经网络表示的AdS/CFT对应，并通过学习过程中的边界量子场论的响应给定的数据集，展示了批量度量函数的出现。出现的径向方向的散装确定的层的深度，和网络本身被解释为散装几何形状。我们的网络提供了强耦合系统的数据驱动全息建模。利用具有未知质量和耦合的标量$ϕ^4$理论，在具有黑洞视界的未知弯曲时空中，我们证明了我们的深度学习（DL）框架可以确定适合给定响应数据的它们。首先，我们表明，从边界数据产生的AdS史瓦西时空，我们的网络可以重现度规。其次，我们证明了我们的网络与实验数据作为输入可以确定的体积度规，质量和二次耦合的全息模型。作为例子，我们使用了强关联材料Sm $_{0.6}$ Sr $_{0.4}$ MnO $_3$的磁响应的实验数据。这种AdS/DL对应关系不仅使强相关系统的重力建模成为可能，而且还揭示了AdS和DL中新兴空间的隐藏机制。

英文摘要：

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 $ϕ^4$ 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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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