String Junctions and Holographic Interfaces

TL;DR

This paper explores half-BPS supergravity solutions with multiple asymptotic regions, revealing a star-graph boundary structure, analyzing junctions of conformal field theories, and deriving a simple formula for boundary entropy.

Contribution

It introduces new supergravity solutions with star-graph holographic boundaries and relates them to junctions of self-dual strings and CFTs, providing explicit conditions and entropy calculations.

Findings

Holographic boundary has star-graph structure.

Conditions for solutions reduce to pole and residue relations.

Derived a simple boundary entropy formula.

Abstract

In this paper we study half-BPS type IIB supergravity solutions with multiple $AdS_3\times S^3\times M_4$ asymptotic regions, where $M_4$ is either $T^4$ or $K_3$. These solutions were first constructed in [1] and have geometries given by the warped product of $AdS_2 \times S^2 \times M_4 $ over $\Sigma$, where $\Sigma$ is a Riemann surface. We show that the holographic boundary has the structure of a star graph, i.e. $n$ half-lines joined at a point. The attractor mechanism and the relation of the solutions to junctions of self-dual strings in six-dimensional supergravity are discussed. The solutions of [1] are constructed introducing two meromorphic and two harmonic functions defined on $\Sigma$. We focus our analysis on solutions corresponding to junctions of three different conformal field theories and show that the conditions for having a solution charged only under Ramond-Ramond three-form fields reduce to relations involving the positions of the poles and the residues of the relevant harmonic and meromorphic functions. The degeneration limit in which some of the poles collide is analyzed in detail. Finally, we calculate the holographic boundary entropy for a junction of three CFTs and obtain a simple expression in terms of poles and residues.