FINITENESS OF THE CHERN-SIMONS MODEL IN PERTURBATION-THEORY

The Chern-Simons action in the Landau gauge is characterized by a BRS symmetry and a local dilatation invariance Ward identity whose quantum extension controls the trace anomaly in the flat limit. We show that the trace anomaly corresponds to all orders to operators which are BRS variations and therefore it cannot have contributions from the Chern-Simons gauge-invariant term. This is sufficient to insure the vanishing of the β-function. We further show that, in a renormalization scheme which preserves scale invariance, there are no finite one-loop corrections to the parameters of the model. © 1990.