Aspects of AdS/BCFT

TL;DR

This work expands the AdS/BCFT framework by introducing a dynamical bulk boundary with Neumann conditions, enabling BCFTs on strips, balls, and time-dependent boundaries. It establishes a universal holographic g-theorem, defines a boundary central charge in 3D BCFT, and computes holographic one-point functions and boundary entropies via disk partition functions and entanglement entropy. The authors also explore phase structure through Hawking-Page–like transitions, extend the construction to higher dimensions, and provide a string theory embedding using orientifold surfaces in AdS_4×CP^3. Together, these results deepen the holographic understanding of boundary effects, RG flows, and their geometric duals, with implications for topological censorship and edge-mode physics.

Abstract

We expand the results of arXiv:1105.5165, where a holographic description of a conformal field theory defined on a manifold with boundaries (so called BCFT) was proposed, based on AdS/CFT. We construct gravity duals of conformal field theories on strips, balls and also time-dependent boundaries. We show a holographic g-theorem in any dimension. As a special example, we can define a `boundary central charge' in three dimensional conformal field theories and our holographic g-theorem argues that it decreases under RG flows. We also computed holographic one-point functions and confirmed that their scaling property agrees with field theory calculations. Finally, we give an example of string theory embedding of this holography by inserting orientifold 8-planes in AdS(4)xCP(3).

Figures (10)

• Figure 1: A schematic setup of AdS/BCFT. The CFT lives on $M$, which has the boundary $\partial M$. Its gravity dual is denoted by $N$ and its asymptotically AdS is $M$. The boundary $\partial M$ is extended into the bulk AdS, which constitutes the boundary $Q$.
• Figure 2: The holographic dual of a half line. The spacetime dual to BCFT is restricted to the region $-\infty <\rho <\rho_*$ and is surrounded by the shaded region.
• Figure 3: The holographic dual of a disk.
• Figure 4: The holographic dual of an annulus made by two disconnected surfaces in the bulk.
• Figure 5: The holographic dual of an interval at low temperature (a) and high temperature (b).