Non-Abelian black string solutions of N=(2,0),d=6 supergravity

TL;DR

This paper explores dualities and solution constructions in six-dimensional supergravity theories, deriving relations between different formulations and uplifting five-dimensional solutions to find supersymmetric non-Abelian black string solutions with rich geometric properties.

Contribution

It establishes dualities between different 6D supergravity models, derives solution-generating rules, and constructs new supersymmetric non-Abelian black string solutions by uplifting 5D solutions.

Findings

Duality between two 6D supergravity formulations.

Derived Buscher rules for solution relations.

Constructed supersymmetric non-Abelian black string solutions.

Abstract

We show that, when compactified on a circle, N=(2,0),d=6 supergravity coupled to 1 tensor multiplet and nV vector multiplets is dual to N=(2,0),d=6 supergravity coupled to just nT=nV+1 tensor multiplets and no vector multiplets. Both theories reduce to the same models of N=2,d=5 supergravity coupled to nV5=nV+2 vector fields. We derive Buscher rules that relate solutions of these theories (and of the theory that one obtains by dualizing the 3-form field strength) admitting an isometry. Since the relations between the fields of N=2,d=5 supergravity and those of the 6-dimensional theories are the same with or without gaugings, we construct supersymmetric non-Abelian solutions of the 6-dimensional gauged theories by uplifting the recently found 5-dimensional supersymmetric non-Abelian black-hole solutions. The solutions describe the usual superpositions of strings and waves supplemented by a BPST instanton in the transverse directions. One of the solutions obtained interpolates smoothly between two AdS3xS3 geometries with different radii.