Supersymmetric Chern-Simons Theories with Vector Matter

Abstract: In this paper we discuss SU(N) Chern-Simons theories at level k with both fermionic and bosonic vector matter. In particular we present an exact calculation of the free energy of the N=2 supersymmetric model (with one chiral field) for all values of the 't Hooft coupling in the large N limit. This is done by using a generalization of the standard Hubbard-Stratanovich method because the SUSY model contains higher order polynomial interactions.