Entanglement entropy in higher derivative holography

TL;DR

This paper explores holographic entanglement entropy in higher derivative gravity theories, deriving entangling surface equations and revealing differences from the two derivative case, with specific focus on Gauss-Bonnet gravity.

Contribution

It applies Lewkowycz and Maldacena's method to four derivative gravity, deriving entangling surface equations and connecting them to existing proposals and stress tensor considerations.

Findings

Equations for entangling surfaces in four derivative gravity are derived.

In Gauss-Bonnet gravity, derived equations match previous proposals.

The area functional acts as a counterterm to remove divergences in Euclidean action.

Abstract

We consider holographic entanglement entropy in higher derivative gravity theories. Recently Lewkowycz and Maldacena arXiv:1304.4926 have provided a method to derive the equations for the entangling surface from first principles. We use this method to compute the entangling surface in four derivative gravity. Certain interesting differences compared to the two derivative case are pointed out. For Gauss-Bonnet gravity, we show that in the regime where this method is applicable, the resulting equations coincide with proposals in the literature as well as with what follows from considerations of the stress tensor on the entangling surface. Finally we demonstrate that the area functional in Gauss-Bonnet holography arises as a counterterm needed to make the Euclidean action free of power law divergences.