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

We show that Abelian Higgs Models with a 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)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$U(1)$$\end{document} model and for the SU(2)×U(1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SU(2)\times U(1)$$\end{document} semilocal model with a doublet of complex scalar fields. The variety of known noncommutative self-dual vortices which display a regular behavior when the noncommutativity parameter tends to zero results in this way considerably enlarged.