Non-Abelian Chern-Simons coefficient in the Higgs phase

We calculate the one loop corrections to the Chern-Simons coefficient (Formula presented) in the Higgs phase of Yang-Mills Chern-Simons Higgs theories. When the gauge group is (Formula presented), we show, by taking into account the effect of the would-be Chern-Simons term, that the corrections are always integer multiples of (Formula presented), as they should be for the theories to be quantum-mechanically consistent. In particular, the correction is vanishing for SU(2). The same method can also be applied to the case where the gauge group is (Formula presented). The result for SO(2) agrees with that found in the Abelian Chern-Simons theories. Therefore, the calculation provides us with a unified understanding of the quantum correction to the Chern-Simons coefficient.