Supergravity geometry in superspace

Some aspects of the superspace geometry of supergravity are discussed. It is shown that all the relevant geometrical objects, i.e., connections, torsions and curvatures of the supergravity geometry can be deduced by a reduction procedure from the riemannian theory. This procedure allows one to obtain closed-form expressions for the superspace connections, which are unconnected in the usual superspace formulation of supergravity, arise in a unified way in this picture. The non-vanishing supergravity torsion arises naturally as the /(3, 1) x O(N) subgroup piece of the larger OSp(3, 1/4N) riemannian tangent-space group in the k → O limit. The spontaneous breaking of the riemannian theory is shown to predict precisely the vacuum values of the supergravity torsions which are assumed in the usual superspace formulations of supergravity. (orig.)