Lecture notes on ChernSimons (super)gravities. Second edition (February 2008)
Abstract
This is intended as a broad introduction to ChernSimons 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 Poincare groups. The resulting lagrangian is a ChernSimons 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 offshell 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2005
 arXiv:
 arXiv:hepth/0502193
 Bibcode:
 2005hep.th....2193Z
 Keywords:

 High Energy Physics  Theory
 EPrint:
 Typos corrected and a few referencesadded. LaTeX, 82 pages, no figures