BPS Analysis of Gauge Field-Higgs Models in Non-Anticommutative Superspace

TL;DR

This paper extends BPS equation analysis to gauge field-Higgs models in non-anticommutative superspace, revealing new vortex and monopole solutions influenced by superspace deformation.

Contribution

It introduces deformed BPS equations in supersymmetric gauge-Higgs models and demonstrates the existence of novel vortex and monopole solutions due to superspace deformation.

Findings

Existence of vortex solutions in deformed Abelian Higgs model.

Discovery of new monopole solutions in deformed non-Abelian models.

Deformation parameter influences the properties of BPS solutions.

Abstract

We extend the study of BPS equations in ${\cal N}=1/2$ super Yang-Mills theory to the case of models with gauge symmetry breaking. We first consider an Abelian gauge-Higgs supersymmetric Lagrangian in $d=4$ dimensional Euclidean space obtained by deforming ${\cal N} = 1$ superspace. The supermultiplets include chiral and vector superfields and its bosonic content coincides with that of the Abelian Higgs model where vortex solutions to the BPS equation are known to exist in the undeformed case. We also consider the $d=3$ dimensional reduction of a non-Abelian $d=4$ deformed model and study its deformed BPS equations, showing the existence of new monopole solutions which depend on the deformation parameter.