String junctions and holographic interfaces

Abstract

In this paper we study half-BPS type IIB supergravity solutions with multiple ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{S}^{3}\ifmmode\times\else\texttimes\fi{}{M}_{4}$ asymptotic regions, where ${M}_{4}$ is either ${T}^{4}$ or ${K}_{3}$. These solutions were first constructed in [M. Chiodaroli, M. Gutperle, and D. Krym, J. High Energy Phys. 02 (2010) 066.] and have geometries given by the warped product of ${\mathrm{AdS}}_{2}\ifmmode\times\else\texttimes\fi{}{S}^{2}\ifmmode\times\else\texttimes\fi{}{M}_{4}$ over $\ensuremath{\Sigma}$, where $\ensuremath{\Sigma}$ 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 [M. Chiodaroli, M. Gutperle, and D. Krym, J. High Energy Phys. 02 (2010) 066.] are constructed introducing two meromorphic and two harmonic functions defined on $\ensuremath{\Sigma}$. 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.