On Holographic Entanglement Entropy and Higher Curvature Gravity

TL;DR

The paper analyzes holographic entanglement entropy in higher-curvature bulk gravity, showing that Wald entropy cannot generally reproduce EE. For Lovelock gravity, EE is correctly captured by the intrinsic-curvature JM functional S_JM, with explicit success in d=4 (ads_5) and substantial tests in d=6 (ads_7) under symmetry assumptions; beyond these, bulk-curvature corrections (ΔS) arise, indicating missing contributions in non-symmetric setups. Extensive checks against field theory results via trace anomalies (a,c,B_n charges) demonstrate that S_JM reproduces the universal logarithmic terms for a wide class of entangling surfaces, while anomalies and Graham-Witten analyses underpin the geometric structure. In general curvature-squared theories, the analysis reveals ambiguities and the need for second-order variational principles to uniquely fix the EE functional, with GB gravity providing a concrete resolution linking Wald, JM, and extrinsic-curvature corrections. The work clarifies when a simple Wald-extremization suffices and points to necessary extensions for broader higher-curvature theories and less symmetric configurations, offering a structured path toward a general holographic EE prescription.

Abstract

We examine holographic entanglement entropy with higher curvature gravity in the bulk. We show that in general Wald's formula for horizon entropy does not yield the correct entanglement entropy. However, for Lovelock gravity, there is an alternate prescription which involves only the intrinsic curvature of the bulk surface. We verify that this prescription correctly reproduces the universal contribution to the entanglement entropy for CFT's in four and six dimensions. We also make further comments on gravitational theories with more general higher curvature interactions.