Einstein--Yang--Mills strings

TL;DR

This paper introduces new gravitating vortex solutions in SU(2) Yang-Mills theory coupled with gravity, resembling superconducting cosmic strings with magnetic flux and unique asymptotic behaviors.

Contribution

It presents the first globally regular, cylindrically symmetric, magnetic vortex solutions in pure SU(2) Yang-Mills coupled to gravity, exhibiting novel magnetic and geometric properties.

Findings

Solutions support non-zero chromo-magnetic flux

They have a compact core with a longitudinal magnetic field

Far field solutions tend to Kasner metrics

Abstract

We present globally regular vortex-type solutions for a pure SU(2) Yang-Mills field coupled to gravity in 3+1 dimensions. These gravitating vortices are static, cylindrically symmetric and purely magnetic, and they support a non-zero chromo-magnetic flux through their cross section. In addition, they carry a constant non-Abelian current, and so in some sense they are analogs of the superconducting cosmic strings. They have a compact central core dominated by a longitudinal magnetic field and endowed with an approximately Melvin geometry. This magnetic field component gets color screened in the exterior part of the core, outside of which the fields approach exponentially fast those of the electrovacuum Bonnor solutions with a circular magnetic field. In the far field zone the solutions are not asymptotically flat but tend to vacuum Kasner metrics.