Holographic entanglement plateaux

TL;DR

This paper explores the behavior of holographic entanglement entropy in finite-volume theories, revealing conditions under which the Araki-Lieb inequality saturates and discussing implications for the structure of extremal surfaces and causal wedges.

Contribution

It demonstrates saturation of the Araki-Lieb inequality for large subregions in holographic theories and introduces an infinite set of extremal surfaces in Schwarzschild-AdS geometry.

Findings

Araki-Lieb inequality saturation for large regions

Infinite extremal surfaces in Schwarzschild-AdS

Implications for holographic entanglement entropy calculations

Abstract

We consider the entanglement entropy for holographic field theories in finite volume. We show that the Araki-Lieb inequality is saturated for large enough subregions, implying that the thermal entropy can be recovered from the knowledge of the region and its complement. We observe that this actually is forced upon us in holographic settings due to non-trivial features of the causal wedges associated with a given boundary region. In the process, we present an infinite set of extremal surfaces in Schwarzschild-AdS geometry anchored on a given entangling surface. We also offer some speculations regarding the homology constraint required for computing holographic entanglement entropy.