Self-dual vortices in Abelian Higgs models with dielectric function on the noncommutative plane

Abstract

We show that Abelian Higgs Models with a dielectric function defined on the noncommutative plane enjoy self-dual vorticial solutions. By choosing a partic- ular 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) × U (1) semilocal model with a doublet of complex scalar fields. The variety of known noncommutative self-dual vortices which display a regular behaviorwhenthenoncommutativityparametertendstozero results in this way considerably enlarged.