Abstract
Based on AdS/CFT correspondence, we build a deep neural network to learn black hole metrics from the complex frequency-dependent shear viscosity. The network architecture provides a discretized representation of the holographic renormalization group flow of the shear viscosity and can be applied to a large class of strongly coupled field theories. Given the existence of the horizon and guided by the smoothness of spacetime, we show that Schwarzschild and Reissner-Nordstr\"{o}m metrics can be learned accurately. Moreover, we illustrate that the generalization ability of the deep neural network can be excellent, which indicates that by using the black hole spacetime as a hidden data structure, a wide spectrum of the shear viscosity can be generated from a narrow frequency range. These results are further generalized to an Einstein-Maxwell-dilaton black hole. Our work might not only suggest a data-driven way to study holographic transports but also shed some light on holographic duality and deep learning.
Highlights
The renormalization group (RG) is a physical scheme to understand various emergent phenomena in the world through iterative coarse graining [1,2,3,4]
Using a simple Deep learning (DL) algorithm, we studied an inverse problem of anti–de Sitter/conformal field theory (AdS/CFT): Given the complex frequencydependent shear viscosity of boundary field theories at finite temperatures, can the bulk metrics of black holes be extracted? We showed that Schwarzschild, RN, and EMD metrics can be learned by the deep neural network (DNN) with high accuracy
The network architecture can be taken as a discretized representation of the holographic RG flow of the shear viscosity, supporting the underlying relationship among DL, RG, and gravity
Summary
The renormalization group (RG) is a physical scheme to understand various emergent phenomena in the world through iterative coarse graining [1,2,3,4]. One can expect at least two benefits: It is helpful to understand how the spacetime emerges and can be used to build a data-driven phenomenological model for strongly coupled field theories. The latter was initiated in [28], where the inverse problem of the AdS/CFT is studied, that is, how to reconstruct the spacetime metric from the given field theory data by the DNN which implements the AdS/CFT. The application of holography is anchored partially in the prediction of the nearly perfect fluidity [35], which has been observed in the hot quark gluon plasmas and cold unitary Fermi gases [36] With these in mind, we adapt the complex frequency-dependent shear viscosity as the given field theory data.
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