Einstein equations, supersymmetry, and flat limits of curved superspace

An affine theory of unified interactions is reviewed. Einstein's free gravitational equation emerges as a special case of the proposed equations of motion on superspace. For this example the vacuum is spontaneously broken to be globally Lorentz invariant. Flat superspace is defined and the corresponding algebraic properties studied. Next the graded de Sitter group is introduced and various contractions performed. From these we obtain and discuss supersymmetry as well as some spin-3/2 algebras. Finally, form invariance under Fermi displacements is employed to develop a powerful calculational technique, an example of which is presented in the Appendix