Strings in Yang-Mills-Higgs theory coupled to gravity

TL;DR

This paper constructs explicit non-Abelian string solutions in Einstein-Yang-Mills-Higgs theory with gravity, analyzing their properties and moduli spaces for different numbers of Higgs fields.

Contribution

It provides the first explicit solutions for non-Abelian strings coupled to gravity and explores their moduli spaces, including local and semilocal cases.

Findings

Solutions are explicitly constructed and shown to be non-Abelian.

All zero modes are normalizable with gravity, even for semilocal strings.

The low-energy effective theories for the moduli are derived.

Abstract

Non-Abelian strings for an Einstein-Yang-Mills-Higgs theory are explicitly constructed. We consider N_f Higgs fields in the fundamental representation of the U(1)xSU(N_c) gauge group in order to have a color-flavor SU(N_c) group remaining unbroken. Choosing a suitable ansatz for the metric, Bogomol'nyi-like first order equations are found and rotationally symmetric solutions are proposed. In the N_f = N_c case, solutions are local strings and are shown to be truly non-Abelian by parameterizing them in terms of orientational collective coordinates. When N_f > N_c, the solutions correspond to semilocal strings which, beside the orientational degrees of freedom, acquire additional collective coordinates parameterizing their transverse size. The low-energy effective theories for the correspondent moduli are found, showing that all zero modes are normalizable in presence of gravity, even in the semilocal case.