On new proposal for holographic BCFT

Abstract

This paper is an extended version of our short letter on a new proposal for holographic boundary conformal field, i.e., BCFT. By using the Penrose-Brown-Henneaux (PBH) transformation, we successfully obtain the expected boundary Weyl anomaly. The obtained boundary central charges satisfy naturally a c-like theorem holographically. We then develop an approach of holographic renormalization for BCFT, and reproduce the correct boundary Weyl anomaly. This provides a non-trivial check of our proposal. We also investigate the holographic entanglement entropy of BCFT and find that our proposal gives the expected orthogonal condition that the minimal surface must be normal to the spacetime boundaries if they intersect. This is another support for our proposal. We also find that the entanglement entropy depends on the boundary conditions of BCFT and the distance to the boundary; and that the entanglement wedge behaves a phase transition, which is important for the self-consistency of AdS/BCFT. Finally, we show that the proposal of arXiv:1105.5165 is too restrictive that it always make vanishing some of the boundary central charges.

Corner contributions to holographic entanglement entropy in AdS4/BCFT3

“…This is confirmed also by the fact that, by taking α → α + c in (5.3) we have z * → +∞. The occurrence of the critical value (5.6) has been observed also in [73].…”

“…The boundary conditions determining Q are crucial in the construction of [63][64][65]. A setup of the correspondence based on a different boundary condition has been recently suggested [72][73][74][75].…”

“…Instead, in [72][73][74] it has been suggested that a consistent AdS/BCFT setup can be defined also by considering the less restrictive boundary condition K = d+1 d T to find Q, obtained by taking the trace of the above Neumann boundary conditions. When the boundary of the BCFT d+1 is a flat d dimensional hyperplane, these two prescriptions provide the same Q ≡ Q.…”

“…Instead, in [72][73][74] it has been proposed to employ the less restrictive boundary condition K = d+1 d T to find Q. When the boundary of the BCFT 3 is flat, both these prescriptions provides the half plane Q = Q given by (4.3).…”

“…By using instead the boundary conditions K = d+1 d T , the relations q = a = f α (π/2) have been obtained [72][73][74]. Notice that the relation q = a is not true for a free scalar [49,56,65].…”