Holographic entanglement entropy in AdS4/BCFT3 and the Willmore functional

Abstract

We study the holographic entanglement entropy of spatial regions having arbitrary shapes in the AdS 4 /BCFT 3 correspondence with static gravitational backgrounds, focusing on the subleading term with respect to the area law term in its expansion as the UV cutoff vanishes. An analytic expression depending on the unit vector normal to the minimal area surface anchored to the entangling curve is obtained. When the bulk spacetime is a part of AdS 4 , this formula becomes the Willmore functional with a proper boundary term evaluated on the minimal surface viewed as a submanifold of a three dimensional flat Euclidean space with boundary. For some smooth domains, the analytic expressions of the finite term are reproduced, including the case of a disk disjoint from a boundary which is either flat or circular. When the spatial region contains corners adjacent to the boundary, the subleading term is a logarithmic divergence whose coefficient is determined by a corner function that is known analytically, and this result is also recovered. A numerical approach is employed to construct extremal surfaces anchored to entangling curves with arbitrary shapes. This analysis is used both to check some analytic results and to find numerically the finite term of the holographic entanglement entropy for some ellipses at finite distance from a flat boundary.

Complexity in the presence of a boundary

“…This "CV subregion complexity" requires first to compute the minimal area surface anchored to the given subregion, whose area provides its holographic entanglement entropy through the Ryu-Takayanagi (RT) prescription [48]. These minimal area "RT surfaces" in the context of AdS/BCFT have been studied extensively [13,14,24,[49][50][51][52][53][54]. The holographic CV subregion complexity is then calculated from the volume of the intersection of the maximal time slice considered in section 2.2, with the spacetime region delimited by the RT surface of the given subregion.…”

Relating bulk to boundary entanglement

“…For a given theory, the corresponding boundary corner function b (B) (θ) depends on the opening angle θ of the corner adjacent to the physical boundary and on the boundary conditions B. Our bulk-boundary relation connects the universal bulk and boundary corner terms for a family of theories (20). The relation applies for boundary theories with "mixed" BCs, such that for bCFTs the Euler boundary central charge vanishes a = 0, see (8).…”

“…These lead to a new type of corner term that is distinct from the corner terms that have been extensively studied in the bulk. The entanglement entropy of such boundary corners has been studied for non-interacting CFTs [8,14,15], certain interacting large-N superconformal gauge theories via the AdS d+1 /bCFT d correspondence [16][17][18][19][20], and a special class of Lifshitz theories [21]. For non-interacting CFTs we find that the boundary corner functions are directly related to the bulk corner function via simple relations.…”

Weyl Anomaly and Vacuum Magnetization Current of M5‐brane in Background Flux

“…The duality has been extensively studied in the literature, with many interesting results obtained. See, for example [75][76][77][78][79][80][81][82][83][84][85].…”