Free-kick condition for entanglement entropy in higher curvature gravity

TL;DR

This paper proposes a new boundary condition, called the free-kick condition, to correctly compute entanglement entropy in higher-curvature gravity theories, and demonstrates its effectiveness in a specific black hole model.

Contribution

It introduces the free-kick condition as a boundary condition for extremal surfaces in higher-curvature gravity, improving entanglement entropy calculations.

Findings

The free-kick condition aligns holographic entanglement entropy with CFT results.

Application to hairy black holes in new massive gravity confirms the prescription's validity.

The method resolves ambiguities in higher-derivative gravity entanglement computations.

Abstract

In order to compute the entanglement entropy for a given region in a theory with an Einstein gravity dual, the Ryu-Takayanagi prescription tells us that we must compute the the area of an extremal surface anchored to the entangling region. However, if the dual gravity theory receives higher-curvature corrections we are compelled to extremize a quantity which is no longer given by the area but a higher-derivative functional. Hence, in order to find the extremal surface that yields the correct value of the entanglement entropy, we must include an additional boundary condition to the problem. We claim that the additional condition can be fixed by demanding that the relationship between the bulk depth and the size of the entangling region is the one induced by geodesics, we call this the free-kick condition. We implement this prescription in the computation of the entanglement entropy of the hairy black hole in new massive gravity, and find a perfect agreement with conformal field theory expectations.