Checking volume-law entropy with HRT surfaces

TL;DR

This paper demonstrates that the Hubeny-Rangamani-Takayanagi prescription yields volume-law entanglement entropy for large subregions in static black brane spacetimes, aligning with expectations from field theory.

Contribution

It provides a formal verification that holographic entanglement entropy follows a volume law for a broad class of subregions beyond constant time slices.

Findings

HRT surfaces produce volume-law entropy in large subregions.

The result applies to symmetric and strip-shaped subregions.

Field-theoretic arguments support the holographic findings.

Abstract

We check formally that the Hubeny-Rangamani-Takayanagi prescription for holographic entanglement entropy -- when applied to a static black brane spacetime and to a wide class of subregions that do not lie on a constant time slice -- gives rise to volume-law entropy in the limit of large subregion. By volume-law entropy, we mean that the entanglement entropy scales with the volume of the projection of the boundary subregion onto a static time slice with respect to the boundary thermal state (with the same coefficient as in the volume law on the static time slice). Our result applies to subregions that have reflection symmetry as well as strips, and we also present field-theoretic arguments in support of our holographic findings.