Exact half-BPS string-junction solutions in six-dimensional supergravity

TL;DR

This paper constructs explicit half-BPS supergravity solutions in six dimensions with multiple AdS_3 x S^3 regions, describing string junctions and their holographic duals, with detailed moduli space characterization.

Contribution

It provides the most general local solutions parametrized by harmonic and holomorphic functions, and constructs globally regular solutions with multiple asymptotic regions in six-dimensional supergravity.

Findings

Explicit formulas for supergravity fields in terms of moduli.

Solutions describe near-horizon geometries of string junctions.

Moduli space dimension matches charge and scalar counting.

Abstract

We construct SO(2,1) x SO(3)-invariant half-BPS solutions in six-dimensional (0,4) supergravity with m tensor multiplets. The space-time manifold of each one of these solutions consists of an AdS_2 x S^2 warped over a Riemann surface Sigma with boundary. The most general local solution is parametrized by one real harmonic function, and m+2 holomorphic functions which are subject to a quadratic constraint and a hermitian inequality, both of which are manifestly SO(2,m) invariant. Imposing suitable conditions on these harmonic and holomorphic functions, we construct globally regular supergravity solutions with N distinct AdS_3 x S^3 asymptotic regions and contractible Sigma. These solutions have an intricate moduli space, whose dimension equals 2(m+1)N -m-2 and matches the counting of three-form charge vectors and un-attracted scalars of the tensor multiplet. Exact explicit formulas for all supergravity fields are obtained in terms of the moduli. Our solutions give the near-horizon geometries for junctions of N self-dual strings in six dimensions, and are holographic duals to CFTs defined on N half-planes which share a common interface line. For m=5, the solutions lift to quarter-BPS solutions for six-dimensional (4,4) supergravity.