Gauged merons

TL;DR

This paper introduces a new class of regular gauged meron solutions in the planar Skyrme model with fractional topological charges, revealing unique interaction patterns and flux quantization mechanisms.

Contribution

It constructs and numerically analyzes gauged merons with fractional charges, exploring their interactions and flux quantization in the strong coupling limit.

Findings

Gauged merons have finite energy and quantized magnetic flux.

They exhibit short-range repulsion and long-range attraction.

Flux quantization relates to the Poincaré index of the Skyrme field components.

Abstract

We construct new class of regular soliton solutions of the gauged planar Skyrme model on the target space $S^2$ with fractional topological charges in the scalar sector. These field configurations represent Skyrmed vortices, they have finite energy and carry topologically quantized magnetic flux $\Phi=2\pi n$ where $n$ is an integer. Using a special version of the product ansatz as guide, we obtain by numerical relaxation various multimeron solutions and investigate the pattern of interaction between the fractionally charged solitons. We show that, unlike the vortices in the Abelian Higgs model, the gauged merons may combine short range repulsion and long range attraction. Considering the strong gauge coupling limit we demonstrate that the topological quantization of the magnetic flux is determined by the Poincar\'{e} index of the planar components $\phi_\perp = \phi_1+i\phi_2$ of the Skyrme field.