On generalized gravitational entropy, squashed cones and holography

TL;DR

This paper investigates generalized gravitational entropy in higher derivative gravity theories dual to 4D CFTs, deriving universal entanglement entropy terms for various surfaces using squashed cone regularization and holographic methods.

Contribution

It introduces a regularization approach for squashed cones in higher derivative gravity and derives universal entanglement entropy terms for spherical and cylindrical surfaces.

Findings

Universal entanglement entropy terms are derived for spherical and cylindrical surfaces.

Wald entropy in regularized geometries matches universal entanglement entropy.

Derived entangling surface equations in Gauss-Bonnet holography.

Abstract

We consider generalized gravitational entropy in various higher derivative theories of gravity dual to four dimensional CFTs using the recently proposed regularization of squashed cones. We derive the universal terms in the entanglement entropy for spherical and cylindrical surfaces. This is achieved by constructing the Fefferman-Graham expansion for the leading order metrics for the bulk geometry and evaluating the generalized gravitational entropy. We further show that the Wald entropy evaluated in the bulk geometry constructed for the regularized squashed cones leads to the correct universal parts of the entanglement entropy for both spherical and cylindrical entangling surfaces. We comment on the relation with the Iyer-Wald formula for dynamical horizons relating entropy to a Noether charge. Finally we show how to derive the entangling surface equation in Gauss-Bonnet holography.