Skyrmion--Anti-Skyrmion Chains

TL;DR

This paper constructs and analyzes static axially symmetric Skyrmion--anti-Skyrmion chain solutions, revealing their topological properties and similarities with monopole pairs, for various winding numbers and solution types.

Contribution

It introduces numerical solutions for Skyrmion--anti-Skyrmion chains characterized by two integers, expanding understanding of their topological structures and existence conditions.

Findings

Chains exist for winding number |n| ≥ 2 without mass term.

Configurations have zero topological charge for even m.

Odd m chains have topological charge n.

Abstract

Static axially symmetric sphaleron-type solutions describing chains of interpolating Skyrmion--anti-Skyrmions have been constructed numerically. The configurations are characterized by two integers n and m, where $\pm n$ are the winding numbers of the constituent Skyrmion and anti-Skyrmion and the second integer m defines type of the solution, it has zero topological charge for even m and for odd values of m the Skyrmion--anti-Skyrmion chain has topological charge n. For the vanishing mass term we confirm the existence of such chain solutions for winding number $|n| \ge 2$. The similarity with monopole--anti-monopole pairs is highlighted.