Solitons in 1+1 Dimensional Gauged Sigma Models

TL;DR

This paper investigates soliton solutions in 1+1 dimensional gauged sigma models derived from 2+1 dimensions, revealing their properties, conserved charges, and exact solutions that saturate the Bogomol'nyi bound.

Contribution

It introduces the analysis of solitons in reduced 1+1 dimensional gauged sigma models, connecting their properties to higher-dimensional counterparts and providing exact solutions.

Findings

Bogomol'nyi bound expressed via two conserved charges

Purely magnetic vortices become charged solitons in 1+1D

Exact static soliton solutions saturating the bound

Abstract

We study soliton solutions in 1+1 dimensional gauged sigma models, obtained by dimensional reduction from its 2+1 dimensional counterparts. We show that the Bogomol'nyi bound of these models can be expressed in terms of two conserved charges in a similar way to that of the BPS dyons in 3+1 dimensions. Purely magnetic vortices of the 2+1 dimensional completely gauged sigma model appear as charged solitons in the corresponding 1+1 dimensional theory. The scale invariance of these solitons is also broken because of the dimensional reduction. We obtain exact static soliton solutions of these models saturating the Bogomol'nyi bound.