# Gauged Sigma Models and Magnetic Skyrmions

## TL;DR

This paper introduces a gauged non-linear sigma model that unifies the description of magnetic skyrmions with arbitrary Dzyaloshinskii-Moriya interactions on Riemann surfaces, providing explicit solutions and applications to impurities.

## Contribution

It formulates a gauged sigma model linking magnetic skyrmions and gauge fields, deriving explicit solutions for the Bogomol'nyi equations on Riemann surfaces.

## Key findings

- Explicit solutions to Bogomol'nyi equations for the model.
- Unified framework for skyrmions with Dzyaloshinskii-Moriya interactions.
- Applications to impurity studies in magnetic materials.

## Abstract

We define a gauged non-linear sigma model for a 2-sphere valued field and a $SU(2)$ connection on an arbitrary Riemann surface whose energy functional reduces to that for critically coupled magnetic skyrmions in the plane, with arbitrary Dzyaloshinskii-Moriya interaction, for a suitably chosen gauge field. We use the interplay of unitary and holomorphic structures to derive a general solution of the first order Bogomol'nyi equation of the model for any given connection. We illustrate this formula with examples, and also point out applications to the study of impurities