The Chern-Simons coefficient in supersymmetric Yang-Mills Chern-Simons theories

We study one-loop corrections to the Chern-Simons coefficient κ = k/4π in N = 1, 2, 3 supersymmetric Yang-Mills Chern-Simons systems. In the pure bosonic case, the shift of the parameter k is known to be k → k + c_v, where c_v is the quadratic Casimir of the gauge group. In the N = 1 case, the fermionic contribution cancels the bosonic contribution by half and the shift is k → k + c_v/2, making the theory anomalous if c_v is odd. In the N = 2, 3 cases, the fermionic contribution cancels the bosonic contribution completely and there is no correction. We also calculate the mass corrections, and show that the supersymmetry is preserved. As the matter fields decouple from the gauge field in the pure Chern-Simons limit, this work sheds some light on the regularization dependency of the correction in pure Chern-Simons systems. We also discuss the implication to the case when the gauge symmetry is spontaneously broken by the Higgs mechanism.