Vacuum and Vortices in Inhomogeneous Abelian Higgs Model

TL;DR

This paper explores inhomogeneous Abelian Higgs models with magnetic impurities, revealing new vacuum solutions with zero energy and analyzing vortex effects numerically, extending understanding of inhomogeneous gauge theories.

Contribution

It introduces a novel inhomogeneous vacuum solution with zero energy in the Abelian Higgs model and studies vortex solutions under impurity effects.

Findings

New inhomogeneous broken vacuum with zero energy identified.

Vortex solutions affected by impurities are numerically characterized.

The model admits an extended supersymmetric formulation despite inhomogeneity.

Abstract

The inhomogeneous abelian Higgs model with a magnetic impurity in the BPS limit is studied for both relativistic and nonrelativistic regimes. Though the symmetry of spatial translation is broken by inhomogeneity, extension to an $\mathcal{N}=1$ supersymmetric theory is admitted. The quartic scalar potential has minimum value depending on strength of the impurity but possesses broken phase at spatial asymptote. The vacuum configuration of broken phase can be neither a constant nor the minimum of the scalar potential, but is found as a nontrivial solution of the Bogomolny equations. While its energy density and magnetic field are given by the function of spatial coordinates, the energy and magnetic flux remain zero. The sign of the magnetic impurity term allows either a BPS sector or anti-BPS sector but not both. Thus the obtained solution is identified as the new inhomogeneous broken vacuum of minimum zero energy. In the presence of rotationally symmetric Gaussian type inhomogeneity, topological vortex solutions are also obtained and the effects of the impurity to the vortex are numerically analyzed.