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

TL;DR

This paper investigates contractions of the superalgebra $osp(1|32)  osp(1|32)$ to find an algebra suitable for $D=11$ supergravity, concluding that such a contraction cannot trivialize the supergravity three-form.

Contribution

It demonstrates that the only contraction of $osp(1|32)  osp(1|32)$ leading to a fermionic extension of the M-theory superalgebra does not trivialize the supergravity three-form.

Findings

The only contracted superalgebra does not trivialize the three-form.

$D=11$ supergravity cannot be obtained via contraction of $osp(1|32)  osp(1|32)$.

Contractions do not produce a suitable gauge algebra for $D=11$ supergravity.

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 $osp(1|32) \oplus osp(1|32)$.