Vortex Strings and Nonabelian sine-Gordon Theories

TL;DR

This paper extends the Lund-Regge vortex string model to n dimensions, linking vortex dynamics to nonabelian sine-Gordon equations and demonstrating their integrability, with explicit solutions derived for vortex configurations.

Contribution

It introduces a generalized n-dimensional vortex equation as a nonabelian sine-Gordon system and proves its integrability via inverse scattering methods.

Findings

Derived explicit vortex coordinate expressions in terms of nonabelian sine-Gordon variables.

Established the integrability of the n-dimensional vortex equation.

Obtained n-dimensional vortex soliton solutions from nonabelian sine-Gordon solitons.

Abstract

We generalize the Lund-Regge model for vortex string dynamics in 4-dimensional Minkowski space to the arbitrary n-dimensional case. The n-dimensional vortex equation is identified with a nonabelian sine-Gordon equation and its integrability is proven by finding the associated linear equations of the inverse scattering. An explicit expression of vortex coordinates in terms of the variables of the nonabelian sine-Gordon system is derived. In particular, we obtain the n-dimensional vortex soliton solution of the Hasimoto-type from the one soliton solution of the nonabelian sine-Gordon equation.