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On New Proposal for Holographic BCFT

Chong-Sun Chu, Rong-Xin Miao, Wu-Zhong Guo

TL;DR

This work introduces a new holographic BCFT dual in which the bulk boundary Q is fixed by a traceless Brown-York condition, enabling nontrivial boundary Weyl anomalies for 3d and 4d BCFT and a unified treatment of general boundary shapes. Through PBH transformations and holographic renormalization, the authors derive boundary anomaly formulas parameterized by ρ_*, and show consistency between embedding universality and anomaly matching. They extend the framework to general boundary conditions by including intrinsic curvature terms on Q, obtaining independent boundary central charges and demonstrating how these charges depend on ρ_* and λ. The holographic entanglement entropy exhibits boundary-induced effects, including orthogonality of minimal surfaces at intersections with Q and a phase transition in entanglement wedges, revealing rich interplay between geometry, boundary data, and quantum information in 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.

On New Proposal for Holographic BCFT

TL;DR

This work introduces a new holographic BCFT dual in which the bulk boundary Q is fixed by a traceless Brown-York condition, enabling nontrivial boundary Weyl anomalies for 3d and 4d BCFT and a unified treatment of general boundary shapes. Through PBH transformations and holographic renormalization, the authors derive boundary anomaly formulas parameterized by ρ_*, and show consistency between embedding universality and anomaly matching. They extend the framework to general boundary conditions by including intrinsic curvature terms on Q, obtaining independent boundary central charges and demonstrating how these charges depend on ρ_* and λ. The holographic entanglement entropy exhibits boundary-induced effects, including orthogonality of minimal surfaces at intersections with Q and a phase transition in entanglement wedges, revealing rich interplay between geometry, boundary data, and quantum information in 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.

Paper Structure

This paper contains 19 sections, 129 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Holographic Boundary Weyl Anomaly
  3. PBH transformation
  4. Boundary Weyl anomaly
  5. Holographic Renormalization of BCFT
  6. 3d BCFT
  7. 4d BCFT
  8. General Boundary Condition
  9. General boundary Weyl anomaly I
  10. General boundary Weyl anomaly II
  11. Holographic Entanglement Entropy
  12. General formula
  13. Boundary effects on entanglement
  14. Entanglement entropy for stripe
  15. Entanglement Wedge
  16. ...and 4 more sections

Figures (5)

  • Figure 1: $OBA > OBA' >OA'$
  • Figure 2: Subsystem $A$ and its mirror image $A'$
  • Figure 3: The minimal surface of stripe.
  • Figure 4: $F(\theta)$ for $d=3$(left) and $d=4$(right)
  • Figure 5: Entanglement wedge for small $A$ and large $A$