  We study one-loop correction to the Chern-Simons coefficient $\kappa=k/4\pi$
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 $k\rightarrow k +
c_v$, 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 $k \rightarrow k+ c_v/2$, 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, showing 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.

High Energy Physics - Theory