EFFECTIVE POTENTIAL FOR A 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 Rξ gauge in the ξ→0 limit. Divergences appearing in the matter sector are regulated via operator regularization. We find no correction 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.