Baby Skyrme models without a potential term

TL;DR

This paper introduces a new family of baby Skyrme models that admit stable topological solitons without requiring a potential term, expanding the understanding of soliton solutions in Skyrme-type theories.

Contribution

The authors develop a one-parameter family of baby Skyrme models without potential terms, demonstrating stable solitons and exact solutions in certain limits, which is a novel property.

Findings

Models satisfy a linear energy bound in topological charge

Existence of compacton solutions in certain parameter regimes

Scale-invariant solitons obtained via Bogomolny equations

Abstract

We develop a one-parameter family of static baby Skyrme models that do not require a potential term to admit topological solitons. This is a novel property as the standard baby Skyrme model must contain a potential term in order to have stable soliton solutions, though the Skyrme model does not require this. Our new models satisfy an energy bound that is linear in terms of the topological charge and can be saturated in an extreme limit. They also satisfy a virial theorem that is shared by the Skyrme model. We calculate the solitons of our new models numerically and observe that their form depends significantly on the choice of parameter. In one extreme, we find compactons while at the other there is a scale invariant model in which solitons can be obtained exactly as solutions to a Bogomolny equation. We provide an initial investigation into these solitons and compare them with the baby Skyrmions of other models.