Nonconimutative Chern-Simons solitons

Abstract

The Chern-Simons theories on a noncommutative plane, which are shown to describe the quantum Hall liquid, are considered. We introduce matter fields fundamentally coupled to the noncommutative ChernSimons field. Exploiting BPS equations for the nonrelativistic Chern-Simons theory, we find the exact solutions of multivortices that are closely packed and exponentially localized. We determine the position, the size, and the angular momentum explicitly. We then construct solutions of two spatially separated vortices, and determine the moduli dependence of the size and the angular momentum. We also consider the relativistic Chern-Simons theory and find nontopological solutions whose properties are similar to the nonrelativistic counterpart. However, unlike the nonrelativistic case, there are two branches of solutions for a given magnetic field and they cease to exist below a certain noncommutativity scale. ©2001 The American Physical Society.