Entanglement entropy from the holographic stress tensor

TL;DR

This paper explores the connection between holographic stress tensors and entanglement entropy in conformal field theories, providing a new perspective on the Ryu-Takayanagi prescription through stress tensor analysis.

Contribution

It demonstrates that the RT entanglement surface equation can be derived from the vanishing of the time-time component of the holographic stress tensor, offering a new justification for the minimal area rule.

Findings

The entangling surface equation matches the condition of zero Brown-York stress tensor component.

Euclidean action methods relate the RT area functional to stress tensor counterterms.

The approach provides a stress tensor-based justification for the minimal area prescription.

Abstract

We consider entanglement entropy in the context of gauge/gravity duality for conformal field theories in even dimensions. The holographic prescription due to Ryu and Takayanagi (RT) leads to an equation describing how the entangling surface extends into the bulk geometry. We show that setting to zero the time-time component of the Brown-York stress tensor evaluated on the co-dimension one entangling surface, leads to the same equation. By considering a spherical entangling surface as an example, we observe that Euclidean action methods in AdS/CFT will lead to the RT area functional arising as a counterterm needed to regularize the stress tensor. We present arguments leading to a justification for the minimal area prescription.