Effective potential for nonrelativistic non-Abelian Chern-Simons matter system in constant background fields

We present the effective potential for nonrelativistic matter coupled to non-Abelian Chern-Simons gauge fields. We perform the calculation using a functional method in constant background fields to satisfy Gauss's law and to simplify the computation. Both the quantum gauge and matter fields are integrated over. The gauge fixing is achieved with an $R_\xi$-gauge in the $\xi\to 0$ limit. Divergences appearing in the matter sector are regulated via operator regularization. We find no corrections to the Chern-Simons coupling constant and the system experiences conformal symmetry breaking to one-loop order except at the known value of self-duality. These results agree with previous analysis of the non-Abelian Aharonov-Bohm scattering.