Bogomol'nyi solitons in a gauged $O(3)$ sigma model

TL;DR

This paper studies topological solitons in a gauged $O(3)$ sigma model with a Maxwell term and potential, revealing stable solutions with flux-dependent size and flux invariance during evolution.

Contribution

It introduces a Bogomol'nyi-type field theory with stable solitons that have arbitrary flux values and analyzes their properties and stability.

Findings

Solitons are stable against rescaling.

Magnetic flux can vary within a finite interval.

Flux remains constant during time evolution.

Abstract

The scale invariance of the $O(3)$ sigma model can be broken by gauging a $U(1)$ subgroup of the $O(3)$ symmetry and including a Maxwell term for the gauge field in the Lagrangian. Adding also a suitable potential one obtains a field theory of Bogomol'nyi type with topological solitons. These solitons are stable against rescaling and carry magnetic flux which can take arbitrary values in some finite interval. The soliton mass is independent of the flux, but the soliton size depends on it. However, dynamically changing the flux requires infinite energy, so the flux, and hence the soliton size, remains constant during time evolution.