Skyrmions confined as beads on a vortex ring

TL;DR

This paper constructs a model where Skyrmions are confined as beads on vortex rings, using quadratic potentials and effective field theories to describe their properties and interactions.

Contribution

It introduces a novel approach to confine Skyrmions as beads on vortex rings within a generalized Skyrme model, including effective field theory formulation.

Findings

Half-Skyrmions appear as beads on vortex rings.

Vortex rings with twisted configurations host multiple halfkinks.

Effective field theory on the torus describes kink dynamics on rings.

Abstract

A very simple, quadratic potential is used to construct vortex strings in a generalized Skyrme model and an additional quadratic potential is used to embed sine-Gordon-type halfkinks onto the string worldline, yielding half-Skyrmions on a string. The strings are furthermore compactified onto a circle and the halfkinks are forced to appear in pairs; in particular 2B halfkinks (half-Skyrmions) will appear as beads on a ring with B being the number of times the host vortex is twisted and also the baryon number (Skyrmion number) from the bulk point of view. Finally, we construct an effective field theory on the torus, describing the kinks living on the vortex rings.