Generalized Maxwell-Higgs vortices in models with enhanced symmetry

TL;DR

This paper explores generalized Maxwell-Higgs models with multiple U(1) symmetries, analyzing static vortex solutions, their magnetic properties, and BPS bounds, revealing new features beyond standard Nielsen-Olesen vortices.

Contribution

It introduces a framework for multi-U(1) Maxwell-Higgs vortices with generalized permeabilities and derives BPS bounds, expanding understanding of vortex solutions in complex gauge theories.

Findings

Derived BPS equations for generalized models

Found solutions with diverse magnetic properties

Compared new solutions to standard Nielsen-Olesen vortices

Abstract

Topological vortices in relativistic gauge theories in flat three-dimensional spacetime are investigated. We consider the symmetry $\rm{U(1)}\times...\times \rm{U(1)}$, and for each $\rm{U(1)}$ subgroup, a complex scalar field transforming under its action is introduced, as well as generalized permeabilities through which the subsystems are coupled. We investigate in detail the features of static, finite energy solutions within this class of generalized Maxwell-Higgs models, and study the effect of the winding numbers in the magnetic properties of each subsystem. A BPS bound and the related first order equations are introduced for a large class of models. Finally, we present some specific models and solve their equations of motion to find solutions engendering many distinct features in relation to each other and to the standard Nielsen-Olesen vortex.