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 A 3 is expressed through a set of one-form gauge fields, B 1 a 1 a 2 , B 1 a 1 ⋯ a 5 , η 1 α , and E a , ψ α . These are associated with the generators of the elements of a family of enlarged supersymmetry algebras E ˜ ( 528 | 32 + 32 ) ( s ) parametrized by a real number s. We study in detail the composite structure of A 3 extending previous results by D’Auria and Fré, stress the equivalence of the above problem to the trivialization of a standard supersymmetry algebra E ( 11 | 32 ) cohomology four-cocycle on the enlarged E ˜ ( 528 | 32 + 32 ) ( s ) superalgebras, and discuss its possible dynamical consequences. To this aim we consider the properties of the first order supergravity action with a composite A 3 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 A 3. The extra gauge symmetries are also present in the so–called rheonomic treatment of the first order D = 11 supergravity action when A 3 is composite. Our considerations on the composite structure of A 3 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 Σ ˜ ( 528 | 32 + 32 ) ( s ) .