A New Proposal for Holographic BCFT

TL;DR

Problem: formulate a holographic dual for BCFT defined on a manifold with boundary. Approach: replace the prior Neumann condition with a mixed boundary condition on the bulk boundary $Q$, fixing $Q$ as a constant mean curvature surface via a traceless Brown–York condition $T_{BY}{}^{\alpha}{}_{\alpha}=2(1-d)K+2dT=0$, yielding a general AdS/BCFT construction that applies to arbitrary boundary $P$ and reduces to disk/half-plane in special cases. Key results: nontrivial boundary Weyl anomalies in $d=3$ and $d=4$ with explicit boundary central charges, holographic entanglement entropy given by the RT formula with an orthogonality constraint at $Q$, and an entanglement wedge that undergoes a phase transition as $A$ approaches the boundary, ensuring bulk reconstructability. Significance: provides a versatile, self-consistent BCFT holography framework with testable predictions, supports a boundary $c$-theorem, and invites extensions to higher dimensions, Lovelock gravity, and condensed-matter applications.

Abstract

We propose a new holographic dual of conformal field theory defined on a manifold with boundaries, i.e. BCFT. Our proposal can apply to general boundaries and agrees with arXiv:1105.5165 for the special case of a disk and half plane. Using the new proposal of AdS/BCFT, we successfully obtain the expected boundary Weyl anomaly and the obtained boundary central charges satisfy naturally a c-like theorem holographically. We also investigate the holographic entanglement entropy of BCFT and find that the minimal surface must be normal to the bulk spacetime boundaries when they intersect. Interestingly,the entanglement entropy depends on the boundary conditions of BCFT and the distance to the boundary. The entanglement wedge has an interesting phase transition which is important for the self-consistency of AdS/BCFT.

Figures (2)

• Figure 1: Subsystem $A$ and its mirror image $A'$
• Figure 2: Entanglement wedge for small $A$ and large $A$