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

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.