Lecture Notes on Chern-simons (super-)gravities

This is intended to be a broad introduction to Chern-Simons gravity and supergravity. The motivation for these theories lies in the desire to have a gauge invariant system –with a fiber bundle formulation– in more than three dimensions, which could provide a firm ground for constructing a quantum theory of the gravitational field. The starting point is a gravitational action which generalizes the Einstein theory for dimensions D > 4 –Lovelock gravity. It is then shown that in odd dimensions there is a particular choice of the arbitrary parameters of the action that makes the theory gauge invariant under the (anti-)de Sitter or the Poincaré groups. The resulting lagrangian is a Chern-Simons form for a connection of the corresponding gauge groups and the vielbein and the spin connection are parts of this connection field. These theories also admit a natural supersymmetric extension for all odd D where the local supersymmetry algebra closes off-shell and without a need for auxiliary fields. No analogous construction is available in even dimensions. A cursory discussion of the unexpected dynamical features of these theories and a number of open problems are also presented. These notes were prepared for the Fifth CBPF Graduate School, held in Rio de Janeiro in July 2004 and will be published in Portuguese [1]. They are a revised version of those prepared for the Villa de Leyva Summer School 2001 and which were published in [2], which were in turn the updated version of the lectures at the La Hechicera School 1999 in Mérida (Venezuela) and at the 20th Particles and Fields Meeting, São Lourenço, Brazil, Oct. 1999 [3].