V. Alan Kostelecky

This work describes the explict construction of the locally SO(4)-invariant, on-shell deSitter supergravity. First, aspects of classical differential geometry used in the construction of local gauge theories are reviewed. Emphasis is placed on fiber bundles and their uses in Yang-Mills and Einstein theories. Next, the extension of the formalism to differential supergeometry is outlined. Applications to extended supergravities are discussed. Finally, the SO(4) deSitter supergravity is obtained by considering a bundle of frames constructed using the orthosymplectic superalgebra osp(4/4). The structure group of this bundle is Sl(2C)(CRTIMES)SO(4) and the tangent space to the base supermanifold is homeomorphic to the coset osp(4/4)/sl(2C)(CRTIMES)so(4). Constraints taken into the Bianchi identities yield a realization of the superalgebra in the function space of connections, vielbeins, curvatures and torsions of the bundle. Auxiliary fields, transformation laws and equations of motion are determined. Consistency of the realization is verified, proving closure of the algebra. The associated Poincare supergravity is obtained by a contraction.