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On the Non-Renormalization Properties of Gauge Theories with Chern-Simons Terms

Oswaldo M. Del Cima·Daniel H. T. Franco·Jose A. Helayel-Neto·Olivier Piguet
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Abstract

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 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.

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Oswaldo M. Del Cima, Daniel H. T. Franco, Jose A. Helayel-Neto, Olivier Piguet. 1998-01-22. On the Non-Renormalization Properties of Gauge Theories with Chern-Simons Terms. https://doi.org/10.1088/1126-6708%2F1998%2F02%2F002

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