Contractions from $osp(1|32)\oplus osp(1|32)$ to the M-theory superalgebra extended by additional fermionic generators

Abstract

We study here the generalized Weimar-Woods contractions of the superalgebra $osp(1|32)\oplus osp(1|32)$ in order to obtain a suitable algebra that could describe the gauge group of $D=11$ supergravity. The contracted superalgebras are assumed to be given in terms of fermionic extensions of the M-theory superalgebra. We show that the only superalgebra of this type obtained by contraction is the only one for which the three-form of $D=11$ supergravity cannot be trivialized. Therefore, $D=11$ supergravity cannot be connected in this way with a contraction of $osp(1|32)\oplus osp(1|32)$.

References in corpus (2)

• Expanding Lie (super)algebras through abelian semigroups
• Expansions of algebras and superalgebras and some applications

Cited by in corpus (1)

• Bosonic D=11 supergravity from a generalized Chern-Simons action