Studies of boundary entropy in AdS/BCFT

Abstract

In this paper we review the AdS/BCFT proposal of T. Takayanagi for holographic description of systems with boundaries, in particular, boundary conformal field theories (BCFTs). Motivated by better understanding of the proposed duality we employ entanglement entropy as a probe of familiar properties of impurities and defects. We discuss configurations, which provide examples of RG flows of the defect entropy as well as RG fixed points. Two interesting observations come out of this analysis of the geometric cartoons of the defect physics. First, entanglement entropy supports the definition of the defect entropy at finite temperature as the Bekenstein-Hawking entropy calculated with respect to a subspace of the horizon. Second, in some examples, geometric data relate entanglement entropy calculations in different dimensions.

Bubble quenches in the AdS/BCFT model

“…In the z → 0 (f (z) → 1) limit one recovers the pure AdS result (7). Some other solutions to boundary conditions (5) were considered in [48,[59][60][61][62][63]. In the next section we will generate time dependent finite temperature solutions applying a conformal transformation.…”

“…Since the Neumann boundary condition should reflect the choice of the dual boundary condition on P , Σ should have a meaning in terms of the CFT data. The exact meaning has not been established so far, but some insight can be obtained by studying the entropy of the defect created by P , as in [44,48,59].…”

“…The AdS d+1 metric is invariant under the d-dimensional conformal group. For example, boosts create lines x = z cot θ(η) moving with constant velocity η in the AdS 3 bulk, intercepting the plane z = 0 at an η-dependent angle [48].…”

“…We will illustrate this argument in an example that follows. See also [48,61,62,[66][67][68] for a similar discussion.…”

“…This setup was dubbed AdS/BCFT as it refers to a gravity dual description of systems with boundaries, which are also amenable to treatment by means of boundary conformal field theories, or BCFTs [45,46]. AdS/BCFT exhibits some characteristic features of BCFTs [44,47,48], although the precise correspondence between the dynamical elements of two approaches has not been established.…”