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**Chern-Simons perturbation theory.**
*(English)*
Zbl 0813.53051

Catto, Sultan (ed.) et al., Differential geometric methods in theoretical physics. Proceedings of the 20th international conference, June 3-7, 1991, New York City, NY, USA. Vol. 1-2. Singapore: World Scientific. 3-45 (1992).

Summary: We study the perturbation theory for three-dimensional Chern-Simons quantum field theory on a general compact three manifold without boundary. We show that after a simple change of variables, the action obtained by BRS gauge fixing in the Lorentz gauge has a superspace formulation. The basic properties of the propagator and the Feynman rules are written in a precise manner in the language of differential forms. Using the explicit description of the propagator singularities, we prove that the theory is finite. Finally the anomalous metric dependence of the 2-loop partition function on the Riemannian metric (which was introduced to define the gauge fixing) can be cancelled by a local counterterm as in the 1-loop case. In fact, the counterterm is equal to the Chern-Simons action of the metric connection, normalized precisely as one would expect based on the framing dependence of Witten’s exact solution.

For the entire collection see [Zbl 0801.00032].

For the entire collection see [Zbl 0801.00032].

### MSC:

53Z05 | Applications of differential geometry to physics |

81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |