Holographic Entanglement Entropy for Brane-World Higher Derivative Gravity

TL;DR

This paper develops a novel method to derive holographic entanglement entropy in brane-world higher derivative gravity, overcoming the splitting problem and extending results to cubic and quartic theories.

Contribution

It introduces a splitting-problem-independent approach to compute holographic entanglement entropy for BWHD gravity, including cubic and quartic cases, using insights from double holography.

Findings

Verified method reproduces known results for curvature-squared gravity.

Derived new entanglement entropy formulas for cubic BWHD gravity.

Performed consistency tests on quartic BWHD gravity entropy results.

Abstract

Due to the splitting problem, it is difficult to derive the holographic entanglement entropy for general higher derivative gravity. Inspired by double holography and renormalized entanglement entropy, we develop a method to derive the generalized gravitational entropy for the brane-world higher derivative (BWHD) gravity. Remarkably, this approach is independent of the splitting problem. The so-called BWHD gravity is an effective theory on the brane, given by the counter terms of holographic renormalization. Interestingly, all solutions to Einstein gravity are also solutions to BWHD gravity. We first verify our approach can derive the correct results for curvature-squared gravity and then derive the holographic entanglement entropy for cubic BWHD gravity, which is the main result of this paper. We also derive the entropy of quartic BWHD gravity in flat space with constant extrinsic curvatures and perform several tests on our results. Finally, we briefly comment on our results.