Om. Delcima et al., ON THE NON-RENORMALIZATION PROPERTIES OF GAUGE-THEORIES WITH A CHERN-SIMONS TERM, JOURNAL OF HIGH ENERGY PHYSICS, (2), 1998, pp. 15-39
Considering three-dimensional Chern-Simons theory, either coupled to m
atter or with a Yang-Mills term, we show the validity of a trace ident
ity, playing the role of a local form of the Callan-Symanzik equation,
in all orders of perturbation theory. From this we deduce the vanishi
ng of the beta-function associated to the Chern-Simons coupling consta
nt and the full finiteness in the case of the Yang-Mills Chern-Simons
theory. The main ingredient in the proof of the latter property is the
noninvariance of the Chern-Simons form under the gauge transformation
s. Our results hold for the three-dimensional Chern-Simons model in a
general Riemannian manifold.