Self-dual non-Abelian vortices in a Φ2 Chern-Simons theory

We study a non-Abelian Chern-Simons gauge theory in 2 + 1 dimensions with the inclusion of an anomalous magnetic interaction. For a particular relation between the Chern-Simons (CS) mass and the anomalous magnetic coupling the equations for the gauge fields reduce from second- to first-order differential equations of the pure CS type. We derive the Bogomolʹnyi-type or self-dual equations for a Φ2 scalar potential, when the scalar and topological masses are equal. The corresponding vortex solutions carry magnetic flux that is not quantized due to the non-topological nature of the solitons. However, as a consequence of the quantization of the CS term, both the electric charge and angular momentum are quantized.