Vortex Solution of a Twisted Baby Skyrme Equation

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.