M-theory backgrounds with 30 Killing spinors are maximally supersymmetric

Abstract

We show that all M-theory backgrounds which admit more than 29 Killing spinors are maximally supersymmetric. In particular, we find that the supercovariant curvature of all backgrounds which preserve 30 supersymmetries, subject to field equations and Bianchi identities, vanishes, and that there are no such solutions which arise as discrete quotients of maximally supersymmetric backgrounds.

37 pages, latex. Minor changes.

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• Static M-horizons
• M-Horizons
• Exact M-Theory Solutions, Integrable Systems, and Superalgebras
• All superalgebras for warped AdS${}_2$ and black hole near horizon geometries
• Holographic duality and applications
• $D=11$ $d{S}_5$ backgrounds with enhanced supersymmetry
• Spinorial geometry, horizons and superconformal symmetry in six dimensions
• Geometrical Aspects of AdS/CFT