On the non-renormalization properties of gauge theories with a Chern-Simons term

Oswaldo M. Del Cima, Daniel H.T Franco, José A Helayël-Neto, Olivier Piguet
1998 Journal of High Energy Physics  
Considering three-dimensional Chern-Simons theory, either coupled to matter or with a Yang-Mills term, we show the validity of a trace identity, playing the role of a local form of the Callan-Symanzik equation, in all orders of perturbation theory. From this we deduce the vanishing of the β-function associated to the Chern-Simons coupling constant 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
more » ... is the noninvariance of the Chern-Simons form under the gauge transformations. Our results hold for the three-dimensional Chern-Simons model in a general Riemannian manifold.
doi:10.1088/1126-6708/1998/02/002 fatcat:lyotiukbqrepfm7w5rzyxtz7j4