NON-ABELIAN CHERN-SIMONS COEFFICIENT IN THE HIGGS PHASE

We calculate the one loop corrections to the Chern-Simons coefficient kappa in the Higgs phase of Yang-Mills Chern-Simons Higgs theories. Wh en the gauge group is SU(N), we show, by taking into account the effec t of the would-be Chern-Simons term, that the corrections are always i nteger multiples of 1/4 pi, as they should be for the theories to be q uantum-mechanically consistent. In particular, the correction is vanis hing for SU(2). The same method can also be applied to the case where the gauge group is SO(N). The result for SO(2) agrees with that found in the Abelian Chern-Simons theories. Therefore, the calculation provi des us with a unified understanding of the quantum correction to the C hern-Simons coefficient.