Brane Dynamics of Holographic BCFTs

TL;DR

Addresses dynamical aspects of $AdS_{d+1}$/BCFT$_d$ with an end-of-the-world brane, analyzing holographic stress-energy tensors, bulk scalar/graviton reflections, Island/BCFT entropy matching, and boundary one-point functions. It performs a detailed gravitational perturbation analysis, identifies the brane-bending mode as a universal helicity-0 contribution, and demonstrates complete reflection of energy flux at the BCFT boundary. It also demonstrates bulk scalar reflection and time evolution numerically, and tests the Island/BCFT correspondence in higher dimensions by matching island-entropy results to holographic entanglement entropy, with explicit leading-area terms and a brane-determined dictionary. Finally, it provides a framework to compute boundary one-point functions holographically in higher dimensions and discusses implications for holographic BCFT dynamics and the black hole information problem.

Abstract

In this paper we study various dynamical aspects of the AdS/BCFT correspondence in higher dimensions. We study properties of holographic stress energy tensor by analyzing the metric perturbation in the gravity dual. We also calculate the stress energy tensor for a locally excited state on a half plane in a free scalar CFT. Both of them satisfy a reflective boundary condition that is expected for any BCFTs. We also study the behavior of the scalar field perturbation in the AdS/BCFT setup and show that they also show complete reflections. Moreover, we find that the entanglement entropy of a BCFT computed from the AdS/BCFT matched with that calculated from the Island formula, which supports the Island/BCFT correspondence in higher dimensions. Finally we show how we can calculate one point functions in a BCFT in our gravity dual.

Figures (11)

• Figure 1: A sketch of AdS/BCFT construction. The gravity dual of a BCFT is given by the red colored region which is surrounded by the boundary where the BCFT is situated (blown colored) and the the end of the world-brane (EOW brane, purple colored).
• Figure 2: A sketch of AdS/BCFT setup.
• Figure 3: The first three eigenfunctions ${\mathcal{R}}(\zeta)$ for $d=3, m^2=0$ and the brane located at $\zeta=\zeta_*=-1/2$, corresponding to $\theta=2\pi/3$. ${\mathcal{R}}(\zeta)$ is normalized so that ${\mathcal{R}}(\zeta_*)=1$.
• Figure 4: Numerical solution for $d=3, m^2=0, \mathbf{k}=0, \lambda_\rho= 5/4$ and initial wave packet with $y_0=4, s=1/8$. In panel (a), only a part of the numerical domain for $0<t<12$ is shown. Panel (b) shows the solution near the reflection point $(t,y)\simeq (8,0)$.
• Figure 5: The dynamics of the brane bending mode in $d=3$ for the brane located at $\zeta=\zeta_* = -1/2$. Panel (a) shows ${\mathcal{R}}^{(\varphi)}(\zeta)$ analyzed in Sec. \ref{['sec:JC']}. Panel (b) shows the time evolution of $Y_{yy}^{(\varphi)}$ with $\mathbf{k}=0$, for which $m^2=0, \lambda_\rho= -1$. The initial field configuration is the same as that for Fig. \ref{['Fig:wave']}.