Holographic BCFTs and Communicating Black Holes

TL;DR

This work constructs a concrete holographic setup for two communicating black holes using a two-boundary BCFT on a strip and two Karch-Randall branes in AdS3. By computing entanglement entropy on both the field theory and gravity sides, the authors demonstrate a Page curve at finite temperature and establish exact agreement between the CFT and gravitational calculations via double holography and quantum extremal surfaces. At zero temperature they uncover a gap $(\frac{c}{16}, \frac{c}{12})$ in the boundary-condition-changing operator spectrum, with the bulk dual being either defect AdS3 or a single-sided black hole depending on $\Delta_{bcc}$, enriching the AdS3/BCFT2 dictionary. The results illuminate how information transfer between braneworld black holes operates in a gravitating bath and provide a tractable laboratory for exploring islands, backreaction, and wedge holography in low dimensions.

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 AdS$_3$/BCFT$_2$ correspondence. For a central charge $c$, we find a gap $(\frac{c}{16},\frac{c}{12})$ in the spectrum of the scaling dimension $Δ_{\text{bcc}}$ of the boundary condition changing operator (which interpolates mismatched boundary conditions on the two boundaries of the BCFT). Depending on the value of $Δ_{\text{bcc}}$, the gravitational dual is either a defect global AdS$_3$ geometry or a single sided black hole, and in both cases there are two Karch-Randall branes.

Figures (9)

• Figure 1: (a) An illustration of wedge holography: the bulk geometry is a part of empty AdS$_{d+1}$ between two end-of-world Karch-Randall branes (black lines), meeting each other on the conformal boundary of AdS$_{d+1}$ at their common boundary (the red dot). The bulk shaded regions behind the branes are removed, leaving only a wedge in the bulk. Wedge holography states that the gravitational physics in the bulk wedge is dual to a $(d-1)$-dimensional conformal field theory living on the red dot (the defect). (b) The wedge holography proposal can be UV regularized by considering a BCFT$_d$ with two boundaries (the two red dots). By sending the separation $L$ between the two boundaries to zero, one goes back to the wedge.
• Figure 2: We consider a two dimensional boundary conformal field theory living on the upper half plane (UHP). The bulk CFT is in the vacuum state, the boundary is specified by the horizontal axis (in red) and the time direction is along the horizontal direction. We consider a constant time slice (dashed black vertical line) which defines the state we are looking at. For this state, we want to compute the entanglement entropy of the region $\mathcal{A}$ (between the blue cross and the boundary) with its complement $\bar{\mathcal{A}}$.
• Figure 3: a) The two Euclidean BCFTs L and R in the TFD state: time evolution is rotation with respect to the origin, hence the red circle is the time evolution of the boundary. The two black dashed lines define the zero time slice. Under the chosen time evolution, L and R evolve clockwise and counter-clockwise respectively, as indicated. We are interested in the entanglement entropy of the subsystem $\mathcal{A}=\mathcal{A}_{L}\cup\mathcal{A}_{R}$ corresponding to the solid green line segments. b) The UHP which results from the conformal mapping of the region outside of the red circle in Fig. \ref{['TFDpre1']}. The circular boundary is mapped to the real axis and infinity is mapped to $\left(0,\frac{1}{2}\right)$. The location of twist operators is mapped to the two blue crosses, separated in the horizontal direction. The branch cut is mapped (and deformed) to the dashed green line connecting the two operators.
• Figure 4: a) CFT on a strip with boundary conditions $a, b$. The time direction is horizontal, and the black dashed line is a constant time slice ($t=0$). A twist operator is inserted at the green cross, separating the subsystem $\mathcal{A}$ and its complement $\bar{\mathcal{A}}$. b) The strip is now conformally transformed to a UHP. The black circle at the origin is a boundary condition changing operator $O_{b\rightarrow a}$. The twist operator is mapped to the green cross. c) The configuration is finally mapped to a UHP with a wedge removed: the twisted upper half plane (TUHP). The boundary consists of two mismatched semi infinite lines, with boundary conditions $a$ and $b$. The twist operator is again mapped to the green cross.
• Figure 5: The two-dimensional CFT on a strip at a finite temperature: the two BCFTs L and R are in the TFD state. Time evolution is rotation with respect to the origin, and the red circles are the time evolution of the two boundaries. The boundary conditions are specified as $a$ and $b$. The black dashed line is the $t=0$ slice, and the choice of time evolution is indicated. We are interested in the entanglement entropy of the subsystem $\mathcal{A} = \mathcal{A}_L \cup \mathcal{A}_R$ corresponding to the solid green line segments connecting the inner boundary and the blue crosses.