Chains of skyrmions

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. For well-chosen periods, the chain of 1-skyrmions appears to be stable to small perturbations. However, as the period increases, the 1-skyrmions clump together, for example giving chains of 2-skyrmions or 4-skyrmions.