On the underlying gauge group structure of D=11 supergravity

The underlying gauge group structure of D = 11 supergravity is revisited. It may be described by a one-parametric family of Lie supergroups Sigma(s) circle times SO(1, 10), s not equal 0. The family of superalgebras E(s) associated to Sigma(s) is given by a family of extensions of the M-algebra {P-a, Q(a), Z(ab), Z(a1)...(a5)} by an,additional fermionic central charge Q'(alpha). The Chevalley-Eilenberg four-cocycle omega(4) similar to Pi(alpha) Lambda Pi(beta) Lambda Pi(a) Lambda Pi(b) Gamma(abalphabeta) on the standard D = 11 supersymmetry algebra may be trivialized on (s), and this implies that the three-form field A(3) of D = 11 supergravity may be expressed as a composite of the Et (s) one-form gauge fields e(a), psi(a), B-ab, B-a1...a5 and eta(alpha). Two superalgebras of E(s) recover the two earlier D'Auria and Fre decompositions of A(3). Another member of E(s) allows for a simpler composite structure for A(3) that does not involve the B-a1...a5 field. Sigma(s) is a deformation of Sigma(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). (C) 2004 Elsevier B.V. All rights reserved.