Holographic duals of Boundary CFTs

TL;DR

The paper advances holographic duals for boundary and interface CFTs by constructing a broad class of regular half-BPS solutions in six-dimensional Type 4b supergravity, with spacetimes of the form $AdS_2 \times S^2$ fibred over a Riemann surface $\Sigma$. It generalizes prior disk and annulus constructions to arbitrary $\Sigma$ with boundary and handles, allowing axion/flux monodromies in the discrete U-duality group $SO(5,m;\mathbb{Z})$, and scalar fields living in the coset $SO(2,m)/SO(2)\times SO(m)$. The authors compute holographic boundary entropies and relate monodromies to three-brane charges, proposing that the most general solutions correspond to near-horizon limits of networks of self-dual strings and three-branes. A detailed annulus example demonstrates BCFT realizations with nontrivial monodromy and elucidates the role of moduli, charges, and degenerations. The work thus provides a robust framework for holographic BCFTs with rich brane/string-network interpretations and paves the way for computing BCFT correlation functions in these backgrounds.

Abstract

New families of regular half-BPS solutions to 6-dimensional Type 4b supergravity with $m$ tensor multiplets are constructed exactly. Their space-time consists of $AdS_2 \times S^2$ warped over a Riemann surface with an arbitrary number of boundary components, and arbitrary genus. The solutions have an arbitrary number of asymptotic $AdS_3 \times S^3$ regions. In addition to strictly single-valued solutions to the supergravity equations whose scalars live in the coset $SO(5,m)/SO(5)\times SO(m)$, we also construct stringy solutions whose scalar fields are single-valued up to transformations under the $U$-duality group $SO(5,m;\bZ)$, and live in the coset $SO(5,m;\bZ)\backslash SO(5,m)/SO(5)\times SO(m)$. We argue that these Type 4b solutions are holographically dual to general classes of interface and boundary CFTs arising at the juncture of the end-points of 1+1-dimensional bulk CFTs. We evaluate their corresponding holographic entanglement and boundary entropy, and discuss their brane interpretation. We conjecture that the solutions for which $Σ$ has handles and multiple boundaries correspond to the near-horizon limit of half-BPS webs of dyonic strings and three-branes.

Figures (10)

• Figure 1: (a) A junction of three self-dual strings in 6-dimensional flat space-time. (b) The corresponding Riemann surface $\Sigma$ for the dual holographic solution with $N=3$ poles. The blue cycles indicate three spheres on which the 3-form charges are supported.
• Figure 2: (a) A self-dual string ending on a three-brane in six dimensions. The charge of the string is absorbed on the three-brane. (b) Riemann surface $\Sigma$ for the dual BCFT solution with one pole. Near the pole a $S^3$ supports the charge, there is a second non-contractible $S^1\times S^2$ cycle.
• Figure 3: (a) A configuration of three-branes and self-dual string networks. In the IR the system flows to a interface CFT. (b) A Riemann surface $\Sigma$ with $N=4$, $\nu=3$ and $g=1$.
• Figure 4: Holographic string-junction solution with $N=3$ asymptotic $AdS_3 \times S^3$ regions localized at the poles $x_n$, with $n=1,2,3$ and $P=4$ auxiliary poles at $y_p$, with $p=1,2,3,4$. Each homology $S^3$ is realized as an $S^2$ fibered over a line interval $C(x_n)$ represented here by a half-circle in blue.
• Figure 5: Contour (in red) around which to integrate $L^6$ to establish residue relation.