(M-theory-)Killing spinors on symmetric spaces

Journal Article · Sat Aug 15 00:00:00 EDT 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4928926· OSTI ID:22479585

Hustler, Noel ^[1]; Lischewski, Andree ^[2]

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1. Maxwell and Tait Institutes, School of Mathematics, University of Edinburgh, King’s Buildings, Edinburgh EH9 3JZ, Scotland (United Kingdom)
2. Humboldt-Universität zu Berlin, Institut für Mathematik, Rudower Chaussee 25, Room 1.310, D12489 Berlin (Germany)

We show how the theory of invariant principal bundle connections for reductive homogeneous spaces can be applied to determine the holonomy of generalised Killing spinor covariant derivatives of the form D = ∇ + Ω in a purely algebraic and algorithmic way, where Ω : TM → Λ{sup ∗}(TM) is a left-invariant homomorphism. Specialising this to the case of symmetric M-theory backgrounds (i.e., (M, g, F) with (M, g) an eleven-dimensional Lorentzian (locally) symmetric space and F an invariant closed 4-form), we derive several criteria for such a background to preserve some supersymmetry and consequently find all supersymmetric symmetric M-theory backgrounds.

• OSTI ID: 22479585
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 8; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
M-THEORY
SPACE
SPINORS
SUPERSYMMETRY