Chains of Skyrmions

TL;DR

This paper demonstrates the existence of Skyrme chains, which are periodic solutions in the Skyrme model, and explores their structure and formation as the period varies, using numerical and analytic methods.

Contribution

It provides the first detailed numerical and analytic investigation of Skyrme chains, including their approximation and behavior as the period increases.

Findings

Skyrme chains exist as topologically nontrivial solutions.

Chains of 1-skyrmions can be approximated by vortex-antivortex pairs.

As the period increases, skyrmions form clumped chains of multiple skyrmions.

Abstract

Skyrme chains are topologically-nontrivial solutions of the Skyrme model which are (quasi-)periodic in one spatial direction. We report numerical and analytic investigations which show that such solutions exist. Chains of 1-skyrmions are reasonably well approximated both as parallel vortex-antivortex pairs, and in terms of the holonomy of Yang-Mills calorons. As the period increases, the 1-skyrmions clump together, for example giving chains of 2-skyrmions or 4-skyrmions.