Topological and nontopological self-dual Chern-Simons solitons in a gauged O(3)<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>σ</mml:mi></mml:math>model

Abstract

We present topological and nontopological self-dual soliton solutions in an O(2) gauged O(3) $\ensuremath{\sigma}$ model on ${\mathrm{R}}_{2}$ with Chern-Simons rather than Maxwell dynamics. These solutions are not vortices in the usual sense in that the magnetic flux is irrelevant to the stability of the topological solitons, which are stabilized by the degree $N$, but it plays a crucial role in the stabilization of the nontopological solitons. It turns out that topological and nontopological solitons of arbitrary vorticity $N$ exist. We have studied both types of vortices with $N=1$ and $N=2$, and the nontopological soliton with $N=0$ numerically. We present analytic proofs for the existence of these topological and nontopological solitons. The qualitative features of the gauged O(3) solitons are contrasted with those of the gauged C${\mathrm{P}}^{1}$ solitons.