Supersymmetric non-Abelian non-commutative Chern-Simons theory

In this work, we study the three-dimensional non-Abelian non-commutative supersymmetric Chern-Simons model with the U(N) gauge group. Using a superfield formulation, we prove that, for the pure gauge theory, the Green functions are one-loop finite in any gauge, if the gauge superpotential belongs to the fundamental representation of u(N); this result also holds when matter in the fundamental representation is included. However, the cancellation of both ultraviolet and ultraviolet/infrared divergences only happens in a special gauge if the coupling of the matter is in the adjoint representation. We also look into the finite one-loop quantum corrections to the effective action: in the pure gauge sector the Maxwell term receives a quantum correction while, in the matter sector, the Chern-Simons term is generated, inducing a shift in the classical Chern-Simons coefficient.