We present all isotropy groups and associated Sigma groups, up to discrete identifications of the component connected to the identity, of spinors of 11-dimensional and type II supergravities. The Sigma groups are products of a Spin group and an R-symmetry group of a suitable lower dimensional supergravity theory. Using the case of SU(4)- invariant spinors as a paradigm, we demonstrate that the Sigma groups, and so the R-symmetry groups of lower dimensional supergravity theories arising from compactifications, have disconnected components. These lead us to discrete symmetry groups reminiscent of R-parity. We examine the role of disconnected components of the Sigma groups in the choice of Killing spinor representatives and in the context of compactifications.
|Classical and Quantum Gravity
|Published - 2009