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

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 $\beta$-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.

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

References in corpus (2)

• A simple remark on three dimensional gauge theories
• Chern-Simons as a geometrical set up for three dimensional gauge theories

Cited by in corpus (12)

• Superconformal Chern-Simons Theories
• Four-Dimensional Superconformal Theories with Interacting Boundaries or Defects
• Marginal Deformations and 3-Algebra Structures
• An algebraic proof on the finiteness of Yang-Mills-Chern-Simons theory in D=3
• Study of Yang-Mills-Chern-Simons theory in presence of the Gribov horizon
• The Jackiw-Pi model and its symmetries
• The ultraviolet and infrared perturbative finiteness of massless QED${}_3$
• The Jackiw-Pi model: classical theory
• Scale Invariance in a Non-Abelian Chern-Simons-Matter Model
• Interpolating gauge-fixing for Yang-Mills-Chern-Simons theory in D=3
• On the trace identity in a model with broken symmetry
• Asymptotic Conformal Invariance in a Non-Abelian Chern-Simons-Matter Model