Self-Dual Vortices in Abelian Higgs Models with Dielectric Function on the Noncommutative Plane

TL;DR

This paper demonstrates the existence of self-dual vortex solutions in Abelian Higgs models with dielectric functions on the noncommutative plane, expanding the variety of known solutions and interpolating between different vortex profiles.

Contribution

It introduces a family of self-dual vortex solutions in noncommutative Abelian Higgs models with dielectric functions, including both $U(1)$ and $SU(2) imes U(1)$ models, enlarging the known solution space.

Findings

Solutions interpolate between Nielsen-Olesen and Chern-Simons vortices.

The solutions are regular as the noncommutativity parameter approaches zero.

The variety of known noncommutative self-dual vortices is significantly increased.

Abstract

We show that Abelian Higgs Models with dielectric function defined on the noncommutative plane enjoy self-dual vorticial solutions. By choosing a particular form of the dielectric function, we provide a family of solutions whose Higgs and magnetic fields interpolate between the profiles of the noncommutative Nielsen-Olesen and Chern-Simons vortices. This is done both for the usual $U(1)$ model and for the $SU(2)\times U(1)$ semilocal model with a doublet of complex scalar fields. The variety of known noncommutative self-dual vortices which display a regular behaviour when the noncommutativity parameter tends to zero results in this way considerably enlarged.