On holographic entanglement entropy and higher curvature gravity

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. A. Fefferman-Graham expansion 40 B. Curved boundaries 41 C. EE in the GB gravity 44 C.1 EE for a sphere with general d 45 C.2 Spherical entangling surfaces beyond GB gravity. 47 C.3 EE for a cylinder with general d 48 D. Curvature tensor for a warped geometry 50 -1 -1If the calculation is done in a Minkowski signature background, the extremal area is only a saddle point. However, if one first Wick rotates to Euclidean signature, the extremal surface will yield the minimal area. In either case, the area must be suitably regulated to produce a finite answer. Note that for a d-dimensional boundary theory, the bulk has d + 1 dimensions while the surface m has d − 1 dimensions. We are using 'area' to denote the (d − 1)-dimensional volume of m.3 Here, we follow closely the notation of [19].

Gravitation from entanglement in holographic CFTs

“…In general, the entanglement entropy functional is known to differ from the Wald functional [34][35][36][37]39] by terms quadratic in the extrinsic curvature of the extremal bulk surface. These terms are important for arbitrarilyshaped entangling surfaces or general states in the CFT.…”

Higher spin entanglement and W N $$ {\mathcal{W}}_{\mathrm{N}} $$ conformal blocks

“…in terms of which the roots of the indicial equation around z = 0 are 4) which implies that the cases where ν is an integer will generically admit logarithmic branches in the solution. Let us first briefly revisit the non-resonant case, i.e.…”

“…One such direction that has been explored is the case in which higher derivative terms are included in the action [4][5][6]. Another is to the case of higher spin gravity, which is the case that we focus on here, in particular its 3d version and corresponding 2d CFT dual.…”

Holographic entanglement entropy in general holographic superconductor models

“…This proposal provides a simple and elegant way to calculate the entanglement entropy of a strongly coupled system which has a gravity dual. Since then, there have been a lot of works studying the entanglement entropy in various gravity theories [37][38][39][40][41][42][43][44][45]. Extending the investigation to the holographic superconductors, Albash and Johnson observed in the metal/superconductor system that the entanglement entropy in superconducting case is always less than the one in the metal phase and the entropy as a function of temperature is found to have a discontinuous slop at the transition temperature T c in the case of the second order phase transition [46].…”