Aspects of holographic entanglement using physics-informed-neural-networks

TL;DR

This work demonstrates that physics-informed neural networks (PINNs) can efficiently compute holographic entanglement measures, enabling minimal-surface problems for arbitrary subregion shapes in asymptotically AdS spacetimes. By validating against analytic results in $\text{AdS}_3/\text{CFT}_2$ and exploring shape dependence in $\text{AdS}_4/\text{CFT}_3$ (ellipses and disks), the authors establish PINNs as a flexible tool for HEE. Extending to entanglement wedge cross sections, they reproduce closed-form EWCS expressions in AdS$_3$ and analyze geometry-driven EWCS behavior in AdS$_4$-Schwarzschild, including inequalities like $E_W\ge I/2$ and horizon-dependent deformations. Overall, the approach offers a robust, adaptable alternative to traditional solvers, with potential extensions to time-dependent and higher-dimensional holographic entanglement problems.

Abstract

We implement physics-informed-neural-networks (PINNs) to compute holographic entanglement entropy and entanglement wedge cross section. This technique allows us to compute these quantities for arbitrary shapes of the subregions in any asymptotically AdS metric. We test our computations against some known results and further demonstrate the utility of PINNs in examples, where it is not straightforward to perform such computations.

Figures (14)

• Figure 1: A schematic illustration of a disk $\mathbb{B}^2$ being mapped to an RT surface via a neural network after training.
• Figure 2:
• Figure 3: Geodesics in $\text{BTZ}$ black hole geometry for different $M$
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• Figure 5: