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

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.

29 pages, 9 figures

References in corpus (3)

• Stationary ring solitons in field theory - knots and vortons
• Gauged Baby Skyrme Model with Chern-Simons term
• Q-balls in Maxwell-Chern-Simons theory

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• $SO(2)$ gauged Skyrmions in $4+1$ dimensions
• A differential relation between the energy and electric charge of a dyon
• Towards spinning $U(1)$ gauged non-topological solitons in the model with Chern-Simons term
• Self-dual solitons in a Born-Infeld baby Skyrme model
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