A. Khare et al., SPONTANEOUS SYMMETRY-BREAKING AND THE RENORMALIZATION OF THE CHERN-SIMONS TERM, Physics letters. Section B, 355(1-2), 1995, pp. 236-240
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.