# Gauged BPS baby Skyrmions with quantised magnetic flux

## TL;DR

This paper introduces a new gauged BPS baby Skyrme model with a linear superpotential equation, enabling magnetic flux quantization and potential application on compact manifolds, advancing the theoretical understanding of topological solitons.

## Contribution

It presents a novel gauged BPS baby Skyrme model with a linear superpotential, allowing magnetic flux quantization and expanding the scope of solvable topological soliton models.

## Key findings

- Magnetic flux is quantized in units of 2π.
- Superpotential equation is linear and fully solvable.
- Model can be defined on compact manifolds without boundary.

## Abstract

A new type of gauged BPS baby Skyrme model is presented, where the derivative term is just the Schroers current (i.e., gauge invariant and conserved version of the topological current) squared. This class of models has a topological bound saturated for solutions of the pertinent Bogomolnyi equations supplemented by a so-called superpotential equation. In contrast to the gauged BPS baby Skyrme models considered previously, the superpotential equation is linear and, hence, completely solvable. Furthermore, the magnetic flux is quantized in units of $2\pi$, which allows, in principle, to define this theory on a compact manifold without boundary, unlike all gauged baby Skyrme models considered so far.