TOPOLOGICAL GRAVITY AND SUPERGRAVITY IN VARIOUS DIMENSIONS

Topological theories of gravity are constructed in odd-dimensional space-times of dimensions 2n + 1, using the Chern-Simons (2n + 1)-forms and with the gauge groups ISO(1, 2n) or SO(1, 2n + 1) or SO(2, 2n). In even dimensions the presence of a scalar field in the fundamental representation of the gauge group is needed, besides the gauge field. Supersymmetrization of the de Sitter groups can be performed up to a maximal dimension of seven, but there is no limit on the super-Poincaré groups. The different phases of the topological theory are investigated. It is argued that these theories are finite. It is shown that the graviton propagates in a perturbative sense around a non-trivial background. © 1990.