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.

• Received 23 December 2016

DOI:https://doi.org/10.1103/PhysRevD.95.085016