Holographic BCFT with a Defect on the End-of-the-World Brane

TL;DR

This work extends AdS/BCFT by introducing a defect that connects two End-of-the-World branes, yielding a tunable BCFT spectrum with the lowest eigenvalue ranging from $-rac{\pi c}{24\Delta x}$ to $0$; it analyzes the bulk geometry, including a possible bulk conical defect, and derives the corresponding BCFT spectrum. It computes holographic entanglement entropy for a BCFT on a strip, revealing three RT phases, including a time-reversal-symmetry-breaking phase, and interprets certain phases as entanglement islands on EOW branes or the defect. The paper also constructs three-dimensional wormhole saddles that connect multiple boundaries, showing such connected saddles exist only for non-unitary BCFTs and are subdominant to factorized saddles. Overall, the defect on EOW branes enables richer boundary dynamics, connects corner BCFT notions to holography, and sheds light on island formulas and nonlocal boundary interactions in holographic BCFT setups.

Abstract

In this paper, we propose a new gravity dual for a $2$d BCFT with two conformal boundaries by introducing a defect that connects the two End-of-the-World branes. We demonstrate that the BCFT dual to this bulk model exhibits a richer lowest spectrum. The corresponding lowest energy eigenvalue can continuously interpolate between $-\frac{πc}{24Δx}$ and $0$ where $Δx$ is the distance between the boundaries. This range was inaccessible to the conventional AdS/BCFT model with distinct boundary conditions. We compute the holographic entanglement entropy and find that it exhibits three different phases, one of which breaks the time reflection symmetry. We also construct a wormhole saddle, analogous to a $3$d replica wormhole, which connects different boundaries through the AdS bulk. This saddle is present only if the BCFT is non-unitary and is always subdominant compared to the disconnected saddle.

Figures (6)

• Figure 1: Sketch of our proposed gravity dual of BCFT. $N$ is the AdS boundary where the BCFT lives. $\Sigma_a$ and $\Sigma_b$ are the EOW branes, and $\Gamma_{(a,b)}$ is the defect connecting them.
• Figure 2: Two EOW branes embedded in Poincare AdS. They intersect in the bulk at an internal angle $\theta_{(1,2)}$ and on the boundary at an internal angle $\gamma_0$. The bulk region is dual to BCFT on the cornered region $N = D$.
• Figure 3: A constant $\tau$ slice of thermal AdS with two EOW branes, $\Sigma_1$ and $\Sigma_2$, meeting at the corner $\Gamma_{(1,2)}$.
• Figure 4: Plot of $\alpha_0$ as a function of $\theta_0$ for various values of tensions.
• Figure 5: Three phases of the RT surfaces for the boundary subregion $A$.