Lecture notes on Chern-Simons (super-)gravities
Year: 2005
Type: preprint
Abstract: : 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
Source: arXiv (Cornell University)
Author: Jorge Zanelli
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1607838929