ON THE NON-RENORMALIZATION PROPERTIES OF GAUGE-THEORIES WITH A CHERN-SIMONS TERM

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.