On the underlying gauge group structure of [formula omitted] supergravity

Abstract

The underlying gauge group structure of D=11 supergravity is revisited. It may be described by a one-parametric family of Lie supergroups Σ˜(s)×⊃SO(1,10), s≠0. The family of superalgebras E˜(s) associated to Σ˜(s) is given by a family of extensions of the M-algebra {Pa,Qα,Zab,Za1⋯a5} by an additional fermionic central charge Qα′. The Chevalley–Eilenberg four-cocycle ω4∼Πα∧Πβ∧Πa∧ΠbΓabαβ on the standard D=11 supersymmetry algebra may be trivialized on E˜(s), and this implies that the three-form field A3 of D=11 supergravity may be expressed as a composite of the Σ˜(s) one-form gauge fields ea, ψα, Bab, Ba1⋯a5 and ηα. Two superalgebras of E˜(s) recover the two earlier D'Auria and Fré decompositions of A3. Another member of E˜(s) allows for a simpler composite structure for A3 that does not involve the Ba1⋯a5 field. Σ˜(s) is a deformation of Σ˜(0), which is singularized by having an enhanced Sp(32) (rather than just SO(1,10)) automorphism symmetry and by being an expansion of OSp(1|32).