English

Lecture notes on Chern-Simons (super-)gravities. Second edition (February 2008)

High Energy Physics - Theory 2008-03-21 v4

Abstract

This is intended as 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 Poincare 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.

Keywords

Cite

@article{arxiv.hep-th/0502193,
  title  = {Lecture notes on Chern-Simons (super-)gravities. Second edition (February 2008)},
  author = {Jorge Zanelli},
  journal= {arXiv preprint arXiv:hep-th/0502193},
  year   = {2008}
}

Comments

Typos corrected and a few referencesadded. LaTeX, 82 pages, no figures

R2 v1 2026-07-22T15:28:48.524Z