Invariant Killing spinors in 11D and type II supergravities

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.

22 pages, typos corrected

References in corpus (36)

• Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi$SB-Resolution of Naked Singularities
• R-parity violating supersymmetry
• Towards the large N limit of pure N=1 super Yang Mills
• Flux compactifications in string theory: a comprehensive review
• The Geometry of D=11 Killing Spinors
• Non-Abelian BPS Monopoles in N=4 Gauged Supergravity
• Complex geometry of conifolds and 5-brane wrapped on 2-sphere
• Maximally supersymmetric solutions of ten- and eleven-dimensional supergravities
• The Geometry of D=11 Null Killing Spinors
• The spinorial geometry of supersymmetric backgrounds
• Hidden Spacetime Symmetries and Generalized Holonomy in M-theory
• On Noncommutative Open String Theories
• Breaking the M-waves
• The spinorial geometry of supersymmetric heterotic string backgrounds
• Holonomy and Symmetry in M-theory
• The spinorial geometry of supersymmetric IIB backgrounds
• Pluecker-type relations for orthogonal planes
• The G_2 spinorial geometry of supersymmetric IIB backgrounds
• Geometry of all supersymmetric type I backgrounds
• Dilatonic p-brane solitons
• Systematics of M-theory spinorial geometry
• Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor
• N=31 is not IIB
• N=31, D=11
• M-theory on manifolds of G2 holonomy: the first twenty years
• Supersymmetric heterotic string backgrounds
• On the absence of BPS preonic solutions in IIA and IIB supergravities
• The holonomy of the supercovariant connection and Killing spinors
• M-theory preons cannot arise by quotients
• IIB solutions with N>28 Killing spinors are maximally supersymmetric
• Solitons in Seiberg-Witten Theory and D-branes in the Derived Category
• Null structure groups in eleven dimensions
• Eight-manifolds with G-structure in eleven dimensional supergravity
• Maximally supersymmetric G-backgrounds of IIB supergravity
• The geometry of extended null supersymmetry in M-theory
• Classification of supersymmetric spacetimes in eleven dimensions

Cited by in corpus (7)

• Generalized structures of ten-dimensional supersymmetric solutions
• All the timelike supersymmetric solutions of all ungauged d=4 supergravities
• M-theory backgrounds with 30 Killing spinors are maximally supersymmetric
• Supersymmetric geometries of IIA supergravity I
• Geometry and symmetries of null G-structures
• Supersymmetric geometries of IIA supergravity III
• Supersymmetric geometries of IIA supergravity II