Invariant Killing spinors in 11D and type II supergravities

TL;DR

This paper classifies all isotropy groups and associated Sigma groups of spinors in eleven-dimensional and type II supergravities, revealing disconnected components that influence symmetry and compactification choices.

Contribution

It provides a comprehensive classification of isotropy and Sigma groups, including their disconnected components, in supergravity theories, highlighting their impact on R-symmetry and compactifications.

Findings

Sigma groups have disconnected components.

Discrete symmetries similar to R-parity are identified.

Disconnected components affect Killing spinor choices and compactifications.

Abstract

We present all isotropy groups and associated $\Sigma$ groups, up to discrete identifications of the component connected to the identity, of spinors of eleven-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 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.