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

TL;DR

This paper investigates how Chern-Simons terms influence the energy, charge, and spin of vortices in 2+1 dimensional gauge models, revealing that energy can decrease with increasing charge, contrary to typical behavior.

Contribution

It demonstrates for the first time that Chern-Simons dynamics can cause electrically charged vortices to have lower energy than neutral ones in 2+1 dimensions.

Findings

Electric charge and spin are induced by Chern-Simons terms.

Vortex energy can decrease as electric charge increases.

Altered energy-spin relationships in vortex solutions.

Abstract

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 $Q_e$. 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. Moreover, the usual energy-spin relationship is likewise altered. We carry out a detailed quantitative analysis of azimuthally symmetric vortices and describe their qualitative features by constructing the solutions numerically.