Dual Geometry of Entanglement Entropy via Deep Learning

Abstract

For a given entanglement entropy of QFT, we investigate how to reconstruct its dual geometry by applying the Ryu-Takayanagi formula and the deep learning method. In the holographic setup, the radial direction of the dual geometry is identified with the energy scale of the dual QFT. Therefore, the holographic dual geometry can describe how the QFT changes along the RG flow. Intriguingly, we show that the reconstructed geometry only from the entanglement entropy data can give us more information about other physical properties like thermodynamic quantities in the IR region.

17 pages, 9 figures

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• Algebraic structures on parallel M2-branes
• Relative entropy and the Bekenstein bound
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• Holographic geometry/real-space entanglement correspondence and metric reconstruction
• Holographic entanglement entropy, Wilson loops, and neural networks