Baby Skyrme models for a class of potentials

TL;DR

This paper explores new types of baby Skyrme models with multi-vacuum potentials, analyzing how symmetry affects skyrmion configurations, their energies, and shapes through numerical methods.

Contribution

It introduces generalized baby Skyrme models with complex potentials and studies their skyrmion configurations and energies, including symmetry-breaking effects.

Findings

Symmetric potentials favor coincident skyrmions as energy minima.

Broken symmetry potentials lead to separated skyrmion configurations.

Numerical results for skyrmions of degrees 1 to 8, including energy and shape analysis.

Abstract

We consider a class of (2+1) dimensional baby Skyrme models with potentials that have more than one vacum. These potentials are generalisation of old and new baby Skyrme models;they involve more complicated dependence on phi_3.We find that when the potential is invariant under phi_3 -> -phi_3 the configuration corresponding to the baby skyrmions lying "on top of each other" are the minima of the energy. However when the potential breaks this symmetry the lowest field configurations correspond to separated baby skyrmions. We compute the energy distributions for skyrmions of degrees between one and eight and discuss their geometrical shapes and binding energies. We also compare the 2-skyrmion states for these potentials. Most of our work has been performed numerically with the model being formulated in terms of three real scalar fields (satisfying one constraint).