(Super-)Gravities of a different sort

TL;DR

This paper reviews gravity theories invariant under de Sitter, anti-de Sitter, or Poincare groups in odd dimensions, highlighting their construction as Chern-Simons and Lovelock gravities, and discusses their supersymmetric extensions and relation to standard theories.

Contribution

It introduces a unified framework for gravity theories based on Chern-Simons and Lovelock constructions in odd dimensions, including their supersymmetric extensions.

Findings

Existence of gravity theories invariant under de Sitter, anti-de Sitter, or Poincare groups in all odd dimensions.

Construction of these theories as Chern-Simons and Lovelock gravities.

Supersymmetric extensions for AdS and Poincare groups, including gauge theories in 11 dimensions.

Abstract

We review the often forgotten fact that gravitation theories invariant under local de Sitter, anti-de Sitter or Poincare transformations can be constructed in all odd dimensions. These theories belong to the Chern-Simons family and are particular cases of the so-called Lovelock gravities, constructed as the dimensional continuations of the lower dimensional Euler classes. The supersymmetric extensions of these theories exist for the AdS and Poincare groups, and the fields are components of a single connection for the corresponding Lie algebras. In 11 dimensions these supersymmetric theories are gauge theories for the osp(1|32) and the M algebra, respectively. The relation between these new supergravities and the standard theories, as well as some of their dynamical features are also discussed.