On entanglement entropy functionals in higher derivative gravity theories

TL;DR

This paper tests proposed entanglement entropy functionals in higher-derivative gravity theories, finding discrepancies between the functional minimization and generalized gravitational entropy methods, and constructs a new functional for quasi-topological gravity.

Contribution

It provides a detailed comparison of entanglement entropy functionals and gravitational entropy methods in higher-derivative theories, revealing inconsistencies and proposing a new functional for quasi-topological gravity.

Findings

Mismatch between surface equations from different methods

Constructed entropy functional for quasi-topological gravity

Functional correctly captures universal terms

Abstract

In arXiv:1310.5713 and arXiv:1310.6659 a formula was proposed as the entanglement entropy functional for a general higher-derivative theory of gravity, whose lagrangian consists of terms containing contractions of the Riemann tensor. In this paper, we carry out some tests of this proposal. First, we find the surface equation of motion for general four-derivative gravity theory by minimizing the holographic entanglement entropy functional resulting from this proposed formula. Then we calculate the surface equation for the same theory using the generalized gravitational entropy method of arXiv:1304.4926. We find that the two do not match in their entirety. We also construct the holographic entropy functional for quasi-topological gravity, which is a six-derivative gravity theory. We find that this functional gives the correct universal terms. However, as in the four-derivative case, the generalized gravitational entropy method applied to this theory does not give exactly the surface equation of motion coming from minimizing the entropy functional.