RENORMALIZATIONS IN ABELIAN CHERN-SIMONS FIELD-THEORIES WITH MATTER

We consider renormalizations in D = 3 abelian Chern-Simons field theories with matter. The anomalous dimensions and beta-functions in a general renormalizable theory with the global SU(n) symmetry are calculated in the leading two-loop approximation. All fixed points are found, and their stability properties are examined. Some of them exhibit the N = 1 and N = 2 supersymmetry. Explicit calculations in terms of the N = 1 and N = 2 superfields confirm the validity of the component-field results. A possible relation to the anyon superconductivity is briefly discussed.