Abstract
We study the AdS/BCFT duality between two-dimensional conformal field theories with two boundaries and three-dimensional anti-de Sitter space with two Karch-Randall branes. We compute the entanglement entropy of a bipartition of the BCFT, on both the gravity side and the field theory side. At finite temperature this entanglement entropy characterizes the communication between two braneworld black holes, coupled to each other through a common bath. We find a Page curve consistent with unitarity. The gravitational result, computed using double-holographically realized quantum extremal surfaces, matches the conformal field theory calculation.At zero temperature, we obtain an interesting extension of the AdS3/BCFT2 correspondence. For a central charge c, we find a gap left(frac{c}{16},frac{c}{12}right) in the spectrum of the scaling dimension ∆bcc of the boundary condition changing operator (which interpolates mismatched boundary conditions on the two boundaries of the BCFT). Depending on the value of ∆bcc, the gravitational dual is either a defect global AdS3 geometry or a single sided black hole, and in both cases there are two Karch-Randall branes.
Highlights
For a central charge c, we find a gap in the spectrum of the scaling dimension ∆bcc of the boundary condition changing operator
Before diving into the computation, we start with a brief review of the realization of the quantum extremal surface prescription [74] in the KR braneworld [7, 48], which is relevant for a holographic computation of the entanglement entropy
The black holes are embedded in two Karch-Randall branes, induced from a bulk AdS3 planar black hole geometry
Summary
We review the relevant background material [20, 48, 50, 52] and set up the context for our calculations. We start with a lightning review of the recently proposed wedge holography [50, 51] from the point of view of Karch-Randall braneworlds [3, 4] and the AdS/CFT correspondence. We come to the system we want to study in this paper: two communicating black holes. This system was first studied in higher dimensions using holographic tools in [48], an approach we review in detail. We discuss the BCFT calculation of entanglement entropy outlined in [52]
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