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 mass-energy 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.