Abstract

We review the often forgotten fact that gravitation theories invariant under local de Sitter, anti-de Sitter or Poincaré 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 Poincaré groups, and the fields are components of a single connection for the corresponding Lie algebras. The need to regularize these theories in order to define conserved charges and thermodynamic functions in asymptotically AdS spacetimes, requires the addition of a very special boundary terms to the action. This modification turn the lagrangian into a transgression. Transgression forms are mathematical objects that play an important role in the Chern-Weil theorems in algebraic topology. Transgressions are invariant functions that depend on two independent connection field, that interact at the boundary of spacetime. In a naive interpretation, the presence of a second connection field with identical quantum numbers as the physical connection might seem embarrassing. However, there is a natural interpretation of this fact recently proposed, whereby our spacetime can be viewed as a subsystem. © 2007 IOP Publishing Ltd.