Exact BPS bound for noncommutative baby Skyrmions

TL;DR

This paper establishes a BPS bound for noncommutative baby Skyrmions, demonstrating their stability and providing exact solutions within a deformed sigma model framework.

Contribution

It introduces a BPS bound for noncommutative baby Skyrmions and proves their stability, with exact solutions identified analytically.

Findings

BPS bound established for noncommutative baby Skyrmions

Exact analytical solutions identified

Baby Skyrmions are stable at unit charge

Abstract

The noncommutative baby Skyrme model is a Moyal deformation of the two-dimensional sigma model plus a Skyrme term, with a group-valued or Grassmannian target. Exact abelian solitonic solutions have been identified analytically in this model, with a singular commutative limit. Inside any given Grassmannian, we establish a BPS bound for the energy functional, which is saturated by these baby Skyrmions. This asserts their stability for unit charge, as we also test in second-order perturbation theory.