Analytic Baby Skyrmions at Finite Density

TL;DR

This paper develops an analytic ansatz for baby Skyrmions in (2+1) dimensions, enabling simplified solutions and stability analysis, including gauged cases with persistent topological currents, useful for testing resurgence phenomena.

Contribution

It introduces a new ansatz reducing the baby Skyrme model to a single equation, allowing explicit analytic solutions with and without gauge fields, advancing understanding of topological and gauge properties.

Findings

Constructed analytic solutions for baby Skyrmions with arbitrary charge.

Analyzed stability and physical properties of the solutions.

Identified the role of Mathieu equation in gauged baby Skyrmions.

Abstract

We introduce a consistent ansatz for the baby Skyrme model in (2+1)-dimensions which is able to reduce the complete set of field equations to just one equation for the profile function in situations in which the baby baryon charge can be arbitrary. Many analytic solutions both with and without the inclusion of the effects of the minimal coupling with the Maxwell field are constructed. Linear stability and other physical properties are discussed. These analytic gauged baby Skyrmions generate a persistent $U(1)$ current which cannot be turned off continuously as it is tied to the topological charge of the baby Skyrmions themselves. In the simplest non-trivial case of a gauged baby Skyrmion, a very important role is played by the Mathieu equation with an effective coupling constant which can be computed explicitly. These configurations are a very suitable arena to test resurgence in a non-integrable context.