Noncommutative Baby Skyrmions

TL;DR

This paper introduces exact noncommutative baby Skyrmion solutions in a deformed sigma model, revealing stable configurations with unique properties due to noncommutativity, and analyzes their interactions and energies.

Contribution

It provides the first explicit analytic noncommutative baby Skyrmion solutions and explores their stability and interactions, expanding understanding of noncommutative solitons.

Findings

Exact analytic noncommutative baby Skyrmions found

Stable against scaling due to noncommutativity

Asymptotic two-Skyrmion interaction characterized

Abstract

We subject the baby Skyrme model to a Moyal deformation, for unitary or Grassmannian target spaces and without a potential term. In the abelian case, the radial BPS configurations of the ordinary noncommutative sigma model also solve the baby Skyrme equation of motion. This gives a class of exact analytic noncommutative baby Skyrmions, which have a singular commutative limit but are stable against scaling due to the noncommutativity. We compute their energies, investigate their stability and determine the asymptotic two-Skyrmion interaction.