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

TL;DR

This paper explores the composite structure of the three-form field in D=11 supergravity, revealing underlying gauge symmetries and proposing an embedding into an extended superspace to better understand its fundamental nature.

Contribution

It demonstrates the composite nature of the three-form field A_3 in D=11 supergravity using enlarged supersymmetry algebras and discusses the implications for gauge symmetries and extended superspace formulations.

Findings

The three-form A_3 can be expressed through one-form gauge fields associated with enlarged supersymmetry algebras.

Extra gauge symmetries ensure the physical degrees of freedom remain unchanged with a composite A_3.

The results suggest a possible embedding of D=11 supergravity into a theory on an extended superspace.

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. These are associated with the generators of the elements of a family of enlarged supersymmetry algebras $\tilde{\mathfrak{E}}^{(528|32+32)}(s)$ parametrized by a real number s. We study in detail the composite structure of A_3 extending previous results by D'Auria and Fr\'e, stress the equivalence of the above problem to the trivialization of a standard supersymmetry algebra ${\mathfrak{E}}^{(11|32)}$ cohomology four-cocycle on the enlarged ${\tilde {\mathfrak{E}}}^{(528|32+32)}(s)$ 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 ${\tilde{\Sigma}}^{(528|32+32)}(s)$.