2008/02/29 by Ulf Gran, U. Gran, J. Gutowski +1
Physics and Astronomy · #Black Holes and Theoretical Physics #Invariant (physics) #Killing spinor #Mathematical physics #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #Physics #Spinor #Supergravity #Supersymmetry #Symmetry group #Theoretical physics #hep-th
paper · pdf · doi:10.1088/0264-9381/26/15/155004
published as Class.Quant.Grav.26:155004,2009 · 22 pages, typos corrected
openalex publication_date 2009/07/08 · arxiv created 2009/07/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present all isotropy groups and associated Σ groups, up to discrete identifications of the component connected to the identity, of spinors of eleven-dimensional and type II supergravities. The Σ 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 Σ 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 Σ groups in the choice of Killing spinor representatives and in Supersymmetric supergravity backgrounds can be categorized into two classes. One class are those backgrounds for which the Killing spinors are invariant under some proper Lie subgroup of the gauge group of the associated theory, and another class are those backgrounds for which the isotropy group of the Killing spinors is the identity. Most