Local gravitational supersymmetry of Chern-Simons theory in the vielbein formalism

We discuss the Chern-Simons theory in three-dimensional curved space-time in the vielbein formalism. Due to the additional presence of the local Lorentz symmetry, beside the diffeomorphisms, we will include a local gravitational supersymmetry (superdiffeomorphisms and super-Lorentz transformations), which allows us to show the perturbative finiteness at all orders. On leave from the Département de Physique Théorique, Université de Genève. Supported by the “Fonds Turrettini” and the “Fonds F. Wurth”. Work supported in part by the “Fonds zur Förderung der Wissenschaftlichen Forschung” under Contract Grant Number P9116-PHY. Work supported in part by the “Fonds zur Förderung der Wissenschaftlichen Forschung” under Contract Grant Number P10268-PHY.