Abstract
We introduce and investigate new models of the Chern–Simons type in the three-dimensional spacetime, focusing on the existence of compact vortices. The models are controlled by potentials driven by a single real parameter that can be used to change the profile of the vortex solutions as they approach their boundary values. One of the models unveils an interesting new behavior, the tendency to make the vortex compact, as the parameter increases to larger and larger values. We also investigate the behavior of the energy density and calculate the total energy numerically.
Highlights
Vortices are topological structures that appear in (2, 1) spacetime dimensions, under the action of a complex scalar field coupled to a gauge field which evolves obeying the local U (1) symmetry
The class of vortices that appears in models driven by the Chern-Simons term presents some interesting features, beyond the fact that they engender a magnetic flux that is quantized by its intrinsic vorticity
A peculiar behavior which deserves to be pointed out is the existence of an electric field and the fact that the magnetic field is related to the electric charge density associated to the Chern-Simons vortex solutions
Summary
Vortices are topological structures that appear in (2, 1) spacetime dimensions, under the action of a complex scalar field coupled to a gauge field which evolves obeying the local U (1) symmetry. One can investigate vortices with the dynamics controlled by the Chern-Simons term, whose general properties where shown in Refs. The first studies considering ChernSimons vortices appeared in Refs. The class of vortices that appears in models driven by the Chern-Simons term presents some interesting features, beyond the fact that they engender a magnetic flux that is quantized by its intrinsic vorticity. Soon after the first works on Chern-Simons vortex [6,7,8], other generalized models that support vortex solutions appeared in Refs. We want to further investigate the presence of vortices in Chern-Simons models, but focusing on generalized models. The first model presents a parameter that controls the potential, which may be increased to make the model become the standard model described in Refs.
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