Noncommutative Chern-Simons solitons - art. no. 025018

The Chern-Simons theories on a noncommutative plane, which are shown to des cribe the quantum Hall liquid, are considered. We introduce matter fields f undamentally coupled to the noncommutative Chern-Simons field. Exploiting B PS equations for the nonrelativistic Chem-Simons theory, we find the exact solutions of multivortices that are closely packed and exponentially locali zed. We determine the position, the size, and the angular momentum explicit ly. We then construct solutions of two spatially separated vortices, and de termine the moduli dependence of the size and the angular momentum. We also consider the relativistic Chern-Simons theory and find nontopological solu tions whose properties are similar to the nonrelativistic counterpart. Howe ver, unlike the nonrelativistic case, there are two branches of solutions f or a given magnetic field and they cease to exist below a certain noncommut ativity scale.