An algebraic proof on the finiteness of Yang-Mills-Chern-Simons theory in D=3
O. M. Del Cima, D. H. T. Franco, J. A. Helayel-Neto, O. Piguet
Abstract
A rigorous algebraic proof of the full finiteness in all orders of perturbation theory is given for the Yang-Mills-Chern-Simons theory in a general three-dimensional Riemannian manifold. We show the validity of a trace identity, playing the role of a local form of the Callan-Symanzik equation, in all loop orders, which yields the vanishing of the beta-functions associated to the topological mass and gauge coupling constant as well as the anomalous dimensions of the fields.
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