Supergravity, supersymmetry: a geometric unitary spinor theory

Abstract

We obtain supersymmetries using spinors as elements of minimal left ideals in Clifford algebra, but without anticommutative analysis. Superalgebras come from an enlarged triality principle. We point out that supersymmetries appear naturally in pseudo-riemannian manifold endowed with spinor bundle and satisfying some Einstein-Hilbert equations (Rarita — Schwinger theory with torsion free connection or with totally antisymmetric torsion tensor). We develop our methods in the space-time background over all, but this approach extends naturally for any dimension and signature and gives the construction of N-supergravitation theories, using always the same geometric scheme.