ar X iv : h ep - t h / 05 02 19 3 v 3 2 6 Fe b 20 08 LECTURE NOTES ON CHERN - SIMONS ( SUPER - ) GRAVITIES Second Edition - February 2008

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, published in Portuguese [1]. These notes were in turn based on a lecture series presented at the Villa de Leyva Summer School 2001 [2], at the La Hechicera School 1999 in Mérida (Venezuela), and at the 20th Particles and Fields Meeting, Sao Lourenço, Brazil, Oct. 1999 [3]. This second edition contains a number of important corrections of errors and obscure points in the previous versions. A number of new references have been added to improve the text. e-mail: z[at]cecs[dot]cl