Entanglement entropy in cubic gravitational theories

TL;DR

This paper derives the holographic entanglement entropy functional for cubic gravitational theories, highlighting differences between minimal and non-minimal splittings, and applies these to specific AdS boundary configurations.

Contribution

It provides the first explicit derivation of the entanglement entropy functional for cubic gravity theories, addressing the splitting problem and comparing different functional forms.

Findings

Both splittings produce different entropy functionals.

Causal wedge inclusion holds for both functionals.

Results are applied to AdS boundary disk and strip configurations.

Abstract

We derive the holographic entanglement entropy functional for a generic gravitational theory whose action contains terms up to cubic order in the Riemann tensor, and in any dimension. This is the simplest case for which the so-called splitting problem manifests itself, and we explicitly show that the two common splittings present in the literature - minimal and non-minimal - produce different functionals. We apply our results to the particular examples of a boundary disk and a boundary strip in a state dual to 4-dimensional Poincar\'e AdS in Einsteinian Cubic Gravity, obtaining the bulk entanglement surface for both functionals and finding that causal wedge inclusion is respected for both splittings and a wide range of values of the cubic coupling.