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

Igor A. Bandos·Jose A. de Azcarraga·Moises Picon·Oscar Varela
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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 Fré, 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 ${\tildeΣ}^{(528|32+32)}(s)$.

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Igor A. Bandos, Jose A. de Azcarraga, Moises Picon, Oscar Varela. 2005-05-05. On the formulation of D=11 supergravity and the composite nature of its three-from field. https://doi.org/10.1016/j.aop.2004.11.016

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