Simple holographic duals to boundary CFTs

TL;DR

The paper extends the class of half-BPS solutions in six-dimensional Type 4b supergravity by allowing AdS_2-cap and AdS_2-funnel singularities, interpreted as fully back-reacted brane configurations with AdS_2 and AdS_2×S^2 worldvolumes. It provides explicit constructions with a single AdS_3×S^3 asymptotic region and multiple caps, derives holographic boundary entropy for BCFT duals, and develops an auxiliary-pole formalism to generate and analyze these generalized solutions. A key finding is that AdS_2-caps yield finite boundary entropy matching BCFT expectations, while AdS_2-funnels introduce additional funnel-related divergences in entanglement entropy, suggesting distinct boundary degrees of freedom. The results illuminate a simple holographic realization of BCFTs in two dimensions and expand the moduli space of regular solutions to include physically meaningful generalized configurations, with implications for U-duality and brane realizations in AdS/CFT.

Abstract

By relaxing the regularity conditions imposed in arXiv:1107.1722 on half-BPS solutions to six-dimensional Type~4b supergravity, we enlarge the space of solutions to include two new half-BPS configurations, which we refer to as the \kap\ and the \funnel. We give evidence that the \kap\ and \funnel\ can be interpreted as fully back-reacted brane solutions with respectively $AdS_2$ and $AdS_2\times S^2$ world volumes. \kap\ and \funnel\ solutions with a single asymptotic $AdS_3 \times S^3$ region are constructed analytically. We argue that \kap\ solutions provide simple examples of holographic duals to boundary CFTs in two dimensions and present calculations of their holographic boundary entropy to support the BCFT dual picture.

Figures (5)

• Figure 1: (a) Junction of a $D1$-brane and a $D5$-brane forming a bound state; (b) The corresponding supergravity solution with two $AdS_2$-caps and one asymptotic $AdS_3 \times S^3$.
• Figure 2: Plot of the metric factors for a solution with two $AdS_2$-cap singularities at $w=\pm 1$ and one asymptotic region at $w=0$. The parameters have the random values $\kappa = 0.74369$ and $\mu = 0.020045$.
• Figure 3: Minimal surface for the holographic entanglement entropy computation; (a) The minimal surface is a point in the $AdS_2$ space; (b) The minimal surface for the $AdS_2$-cap with corresponding cutoff; (c) The minimal surface for the $AdS_2$-funnel with corresponding cutoffs; (d) Corresponding partition of the BCFT.
• Figure 4: Plot of the metric factors for a solution with one $AdS_2$-funnel at $w=i$ and one asymptotic $AdS_3 \times S^3$ region at $w=0$. The parameters have been chosen randomly to have values $\kappa = 0.74369$ and $\mu = 0.020045$.
• Figure 5: (a) The degeneration of an annulus produces an $AdS_2$-funnel. (b) The dividing degeneration of disk produces a $AdS_2$-cap.