On the formulation of D=11 supergravity and the composite nature of its three-form gauge field

Abstract: The underlying gauge group structure of the D=11 Cremmer–Julia–Scherk supergravity becomes manifest when its three-form field A3 is expressed through a set of one-form gauge fields, , , η1α, and Ea, ψα. These are associated with the generators of the elements of a family of enlarged supersymmetry algebras parametrized by a real number s. We study in detail the composite structure of A3 extending previous results by D’Auria and Fré, stress the equivalence of the above problem to the trivialization of a standard supersymmetry algebra cohomology four-cocycle on the enlarged superalgebras, and discuss its possible dynamical consequences. To this aim we consider the properties of the first order supergravity action with a composite A3 field and find the set of extra gauge symmetries that guarantee that the field theoretical degrees of freedom of the theory remain the same as with a fundamental A3. The extra gauge symmetries are also present in the so–called rheonomic treatment of the first order D=11 supergravity action when A3 is composite. Our considerations on the composite structure of A3 provide one more application of the idea that there exists an extended superspace coordinates/fields correspondence. They also suggest that there is a possible embedding of D=11 supergravity into a theory defined on the enlarged superspace . [Copyright &y& Elsevier]