SPONTANEOUS SYMMETRY-BREAKING AND THE RENORMALIZATION OF THE CHERN-SIMONS TERM

We calculate the one-loop perturbative correction to the coefficient o f the Chern-Simons term in non-abelian gauge theory in the presence of Higgs fields, with a variety of symmetry-breaking structures. In the case of a residual U(1) symmetry, radiative corrections do not change the coefficient of the Chem-Simons term. In the case of an unbroken no n-abelian subgroup, the coefficient of the relevant Chem-Simons term ( suitably normalized) attains an integral correction, as required for c onsistency of the quantum theory. Interestingly, this coefficient aris es purely from the unbroken non-abelian sector in question; the orthog onal sector makes no contribution. This implies that the coefficient o f the Chern-Simons term is a discontinuous function over the phase dia gram of the theory.