Vortex Solution of the Gravitational Field Equation of a Twisted Skyrme Strings

TL;DR

This paper explores vortex solutions in a twisted Skyrme model coupled with gravity, analyzing simplified cases without the Skyrme term to understand the effects of twisting on gravitational vortex configurations.

Contribution

It introduces a gravitational vortex solution with a twist in the non-linear sigma model, providing insights into the effects of twisting on vortex structures in gravitational fields.

Findings

Vortex solutions with twist resemble untwisted solutions in the simplified model.

The work advances understanding of twisted vortex configurations in gravitational contexts.

Progress is ongoing in extending these solutions to the full Skyrme model.

Abstract

We construct non-linear sigma model plus Skyrme term (Skyrme model) with a twist in the gravitational field. To simplify the solution, first we examine non-linear sigma model without Skyrme term, in particular with a twist, which comprises a vortex solution with an added dependence on a twist term $mkz$, where $z$ is the vertical coordinate. We find that vortex solution for non-linear sigma model with a twist is similar with vortex solution without a twist. The work is still progress.