Holographic Entanglement Entropy, Field Redefinition Invariance and Higher Derivative Gravity Theories

TL;DR

This paper demonstrates that holographic entanglement entropy calculations in higher derivative gravity theories are invariant under field redefinitions, establishing a consistent method to compute HEE using the Wald entropy functional for these theories.

Contribution

It introduces a fixed recipe for holographic entanglement entropy in $f(R,R_{\mu\nu})$ theories, ensuring invariance under field redefinitions and linking HEE to Wald entropy.

Findings

HEE surfaces have vanishing extrinsic curvature trace.

HEE can be computed using Wald entropy functional.

Results are consistent with FPS and Dong functionals for Einstein backgrounds.

Abstract

It is established that physical observables in local quantum field theories should be invariant under invertible field redefinitions. It is then expected that this statement should be true for the entanglement entropy and moreover that, via the gauge/gravity correspondence, the recipe for computing entanglement entropy holographically should also be invariant under local field redefinitions in the gravity side. We use this fact to fix the recipe for computing holographic entanglement entropy (HEE) for $f(R,R_{\mu\nu})$ theories which could be mapped to Einstein gravity. An outcome of our prescription is that the surfaces that minimize the corresponding HEE functional for $f(R,R_{\mu\nu})$ theories always have vanishing trace of extrinsic curvature and that the HEE may be evaluated using the Wald entropy functional. We show that similar results follow from the FPS and Dong HEE functionals, for Einstein manifold backgrounds in $f(R,R_{\mu\nu})$ theories.