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

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

1997-11-26

arxiv.org/abs/hep-th/9711191v3

JHEP 9802:002,1998

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, Latex. Small changes in the introduction, concerning the citations; two references added, one updated. Some misprint

Scientific paper

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 $\beta$-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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