Effect of Chern-Simons dynamics on the energy of electrically charged and spinning vortices

We study the effect of a Chern-Simons term on the electrically charged and spinning solitons of several U(1) gauged models in 2 + 1 dimensions. These are vortices of complex scalar field theories, both with and without symmetry breaking dynamics, and the O(3) Skyrme model. In all cases the gauge decoupling limits are also considered. It is well known that the effect of the Chern-Simons dynamics is to endow vortices with electric charge Q(e) and spin J, but our main aim here is to reveal a new feature: that the massenergy E of the electrically charged vortex can be lower than that of the electrically neutral one, in contrast to the usual monotonic increase of E with Q(e) and J. These effects of Chern-Simons dynamics were observed previously in 3 + 1 dimensional systems, and the present results can be viewed as corroborating the latter. We carry out a detailed quantitative analysis of azimuthally symmetric vortices and describe their qualitative features by constructing the solutions numerically