Both provide examples of a common principle: the existence of an enlarged superspaces coordinates/fields correspondence by which all the (worldvolume or spacetime) fields of the theory are associated to coordinates of enlarged superspaces. We discuss the role of enlarged superspaces in two seemingly different contexts, the structure of the p-brane actions and that of the Cremmer-Julia-Scherk eleven-dimensional supergravity. The resulting field equations are similar to those of simple supergravity with only a spin-3/2 field appearing in addition to the spin-2 Einstein field, however, supersymmetry invariance seems to play little or no direct role in the present theory. We thus end up with a very simple, geometrical theory which contains far fewer fields that the geometrical work of Arnowitt and Nath while keeping their elegance of formulation. The field equations correctly describe a spin-3/2 field coupled to general relativity, with the correct ''energy-momentum tensor'' of the spin-3/2 field appearing automatically. The theory is also completely basis invariant. The theory is self sourced and more » the spin-3/2 field and usual spin-2 field appear as gauge fields. The Lagrangian is taken to be the scalar curvature of the fiber bundle, in analogy with general relativity with no source terms. It comes in through the commutation relations of the basis vectors in the horizontal lift basis, or through the metric in the local direct-product basis. In the fiber bundle geometry, a spin-3/2 field arises automatically. We develop a new theory of the pure gravitational field by treating superspace as a fiber bundle with space-time as the base space, and Fermi space, with anticommuting Majorana spinor coordinate q/sup i/, as the typical fiber.
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