Vortex Solution of a Twisted Baby Skyrme Equation

TL;DR

This paper investigates twisted baby Skyrmion vortex solutions in a non-linear sigma model with a Skyrme term, analyzing their asymptotic behavior and how their mass per unit length depends on a twist parameter.

Contribution

It introduces a twisted vortex solution in the baby Skyrme model and explores its asymptotic form and mass dependence on the twist parameter.

Findings

Mass per unit length increases roughly linearly with the twist parameter.

Solutions exhibit specific asymptotic behavior influenced by the twist.

The twist term affects the physical properties of the vortex solutions.

Abstract

We examine non-linear sigma (plus Skyrme term) model in flat space, in particular with a twist, which comprises a twisted baby Skyrmion vortex solution with an added dependence on a twist term $mkz$, where $z$ is the vertical coordinate. We find that the solutions should have asymptotic form. We also find that mass per unit length of string, $\mu$, increases roughly linearly with $\zeta$, where $\zeta=4\lambda^2K_s(mk)^2$, $\lambda$ is scaling constant, $K_s$ is Skyrme term, $m$ is integer and $k$ is wave number.