AdS/BCFT with Brane-Localized Scalar Field

TL;DR

<3-5 sentence high-level summary> The paper extends AdS/BCFT by introducing a brane-localized scalar field, dual to a boundary primary operator, and develops explicit gravity solutions in AdS3/BCFT2 that realize boundary RG flows and novel end-of-the-world brane geometries (hemisphere, cone, annulus). It analyzes planar and round branes across dimensions, and studies finite-temperature transitions between connected and disconnected EOW-brane configurations, revealing a confinement/deconfinement-like phase diagram. A Wick-rotated formulation leads to transition matrices and pseudo entropy, with a phase structure reminiscent of measurement-induced phase transitions, suggesting a gravity dual for certain non-unitary open-system dynamics. The results broaden the AdS/BCFT framework, offering tractable models of boundary deformations, holographic entanglement data, and potential connections to Kondo-like physics and quantum information aspects of BCFTs.

Abstract

In this paper, we study the dynamics of end-of-the-world (EOW) branes in AdS with scalar fields localized on the branes as a new class of gravity duals of CFTs on manifolds with boundaries. This allows us to construct explicit solutions dual to boundary RG flows. We also obtain a variety of annulus-like or cone-like shaped EOW branes, which are not possible without the scalar field. We also present a gravity dual of a CFT on a strip with two different boundary conditions due to the scalar potential, where we find the confinement/deconfinement-like transition as a function of temperature and the scalar potential. Finally, we point out that this phase transition is closely related to the measurement-induced phase transition, via a Wick rotation.

Figures (34)

• Figure 1: A sketch of our setup of AdS/BCFT.
• Figure 2: The setup of AdS$_3/$BCFT$_2$ with a planar EOW brane. The red curve shows the end-of-the-world-brane $Q$. The green curves describe the geodesics $\Gamma^{(1,2)}$ which compute the holographic entanglement entropy.
• Figure 3: The profile of $V(\phi)$ (left), $z(\tau)$ (middle) and $\phi(\tau)$ (right) for $\alpha=\lambda=1$. We find $\phi_*\simeq 2.5.$
• Figure 4: The profile of $V(\phi)$ (left), $z(\tau)$ (middle) and $\phi(\tau)$ (right) for $\alpha=1,\mu=2$
• Figure 5: Left figure shows geodesic length (solid line) of $z(\tau)=\tau+\tau^2$ case and plot of $log(2\tau_0/\epsilon)$ (dashed line). Right figure shows the difference between solid line and dashed line.