Non-Abelian vacua in D=5, N=4 gauged supergravity

TL;DR

This paper investigates non-Abelian vacuum solutions in five-dimensional N=4 gauged supergravity, deriving Bogomol'nyi equations and finding regular solutions with specific symmetry properties and supersymmetry preservation.

Contribution

It introduces new supersymmetric non-Abelian background solutions in D=5, N=4 gauged supergravity with detailed analysis of symmetry and supersymmetry conditions.

Findings

Derived Bogomol'nyi equations for the configurations

Found globally regular solutions with specific symmetries

Identified supersymmetry preservation properties of solutions

Abstract

We study essentially non-Abelian backgrounds in the five dimensional N=4 gauged SU(2)$\times$U(1) supergravity. Static configurations that are invariant under either the SO(4) spatial rotations or with respect to the SO(3) rotations and translations along the fourth spatial coordinate are considered. By analyzing consistency conditions for the equations for supersymmetric Killing spinors we derive the Bogomol'nyi equations and obtain their globally regular solutions. The SO(4) symmetric configurations contain the purely magnetic non-Abelian fields together with the purely electric Abelian field and possess two unbroken supersymmetries. The SO(3) configurations have only the non-Abelian fields and preserve four supersymmetries.