SO(3) \times U(1) isometric instantons with non abelian hair in four dimensional string theory

TL;DR

This paper constructs exact four-dimensional string theory backgrounds with non-abelian SU(2) instanton solutions exhibiting SO(3) x U(1) symmetry, derived from a specific coset model and related to semiclassical string solutions.

Contribution

It provides the first exact string vacuum solutions representing non-abelian instantons with SO(3) x U(1) symmetry in four dimensions, derived from a level 81/19 SU(2,1)/U(1) coset model.

Findings

Exact string backgrounds with non-abelian SU(2) instantons are constructed.

The solutions exhibit SO(3) x U(1) isometry and relate to semiclassical string solutions.

The backgrounds include a singular submanifold and are derived from a specific coset model.

Abstract

We compute the exact effective string vacuum backgrounds of the level $k = 81/19 SU(2,1)/U(1)$ coset model. A compact SU(2) isometry present in this seven dimensional solution allows to interpreting it after compactification as a four dimensional non-abelian SU(2) charged instanton with a singular submanifold and an $SO(3) \times U(1)$ isometry. The semiclassical backgrounds, solutions of the type II strings, present similar characteristics.