# Vortices of $SO(2)$ gauged Skyrmions in $2+1$ dimensions

## TL;DR

This paper systematically studies vortices in an $SO(2)$ gauged Skyrme model in 2+1 dimensions, analyzing energy dependence on parameters and topological charge evolution across Maxwell, Chern-Simons, and combined dynamics.

## Contribution

It provides a comprehensive analysis of vortex solutions in the gauged Skyrme model with different gauge dynamics, highlighting novel behaviors like energy discontinuities and non-integer topological charges.

## Key findings

- Energy vs. $\lambda$ plots show discontinuities and branches.
- Topological charge can evolve to non-integer values.
- Contrasts with Abelian Higgs models are established.

## Abstract

Vortices the $SO(2)$ gauged planar Skyrme model, with a) only Maxwell, b) only Chern-Simons, and c) both Maxwell and Chern-Simons dynamics are studied systematically. In cases a) and b), where both models feature a single parameter $\lambda$ (the coupling of the potential term), the dependence of the energy on $\lambda$ is analysed. It is shown that the plots of the energy $vs.$ $\lambda$ feature discontinuities and branches. In case c), the emphasis is on the evolution of the topological charge, taking non-integer values. Throughout, the properties studied are contrasted with those of the corresponding Abelian Higgs models.