On shape dependence of holographic entanglement entropy in AdS4/CFT3

Abstract

Abstract:We study the finite term of the holographic entanglement entropy of finite domains with smooth shapes and for four dimensional gravitational backgrounds. Analytic expressions depending on the unit vectors normal to the minimal area surface are obtained for both stationary and time dependent spacetimes. The special cases of AdS 4 , asymptotically AdS 4 black holes, domain wall geometries and Vaidya-AdS backgrounds have been analysed explicitly. When the bulk spacetime is AdS 4 , the finite term is the Willmore energy of the minimal area surface viewed as a submanifold of the three dimensional flat Euclidean space. For the static spacetimes, some numerical checks involving spatial regions delimited by ellipses and non convex domains have been performed. In the case of AdS 4 , the infinite wedge has been also considered, recovering the known analytic formula for the coefficient of the logarithmic divergence.

Corner contributions to holographic entanglement entropy in AdS4/BCFT3

“…The holographic prescription (1.6) has been applied also for domains A whose boundaries contain singular points [30,[59][60][61][62]. We are interested in the d = 2 case, where the expansion of A[γ ε ] as ε → 0 + for domains A with corners reads…”

“…Numerical checks of these results are performed by constructing the minimal area surfaces corresponding to some finite domains containing corners. In the numerical analysis we have employed Surface Evolver [76,77] to construct the minimal area surfaces, a software which has been already used in [60,61] to study the shape dependence of the holographic entanglement entropy in AdS 4 /CFT 3 .…”

“…Our confidence in this tool relies on the very good results obtained in section 3 for the corner functions in AdS 4 /CFT 3 . In the appendix A we briefly discuss some peculiar features which distinguish our numerical analysis from the one performed in [60,61], where Surface Evolver has been employed to study the shape dependence of the holographic entanglement entropy in AdS 4 /CFT 3 .…”

Analytic black branes in Lifshitz-like backgrounds and thermalization

“…The behavior of the entanglement entropy modeling the thermalization and "quench" processes is a subject of intensive studies during last years, see [36,[38][39][40][41][42] and refs. therein.…”

On shape dependence of holographic entanglement entropy in AdS4/CFT3 with Lifshitz scaling and hyperscaling violation

“…The main result of this manuscript is their expression as (finite) geometrical functionals over the two dimensional surface γ A (orγ A for F A ) viewed as a submanifold of M 3 . The procedure to obtain the finite terms extends the one developed in [68,69] for AdS 4 and in [70] for asymptotically AdS 4 spacetimes. Since the specific details of this analysis depend on the type of divergences occurring in the expansion of the area functional as ε → 0, we will treat the regimes 1 < d θ < 3 and 3 < d θ < 5 separately.…”