Finiteness of Chern-Simons theory and fermion decoupling in 2 + 1-dimensional SU(N) gauge field theory

We discuss the decoupling of heavy fermions in SU(N) gauge field theory (GFT) in 2 + 1-dimensional spacetime. The pure Chern-Simons (CS) theory may be seen as the resulting theory when the charge of the gauge field also goes to infinity. Then the finiteness of the CS theory or the vanishing of the beta function of the CS coefficient ϰcs with or without matter, is proved in this approach.