The geometry of extended null supersymmetry in M-theory

Abstract

For supersymmetric spacetimes in eleven dimensions admitting a null Killing spinor, a set of explicit necessary and sufficient conditions for the existence of any number of arbitrary additional Killing spinors is derived. The necessary and sufficient conditions are comprised of algebraic relationships, linear in the spinorial components, between the spinorial components and their first derivatives, and the components of the spin connection and four-form. The integrability conditions for the Killing spinor equation are also analysed in detail, to determine which components of the field equations are implied by arbitrary additional supersymmetries and the four-form Bianchi identity. This provides a complete formalism for the systematic and exhaustive investigation of all spacetimes with extended null supersymmetry in eleven dimensions. The formalism is employed to show that the general bosonic solution of eleven dimensional supergravity admitting a $G_2$ structure defined by four Killing spinors is either locally the direct product of ${\mathbb{R}}^{1,3}$ with a seven-manifold of $G_2$ holonomy, or locally the Freund-Rubin direct product of $Ad{S}_4$ with a seven-manifold of weak $G_2$ holonomy. In addition, all supersymmetric spacetimes admitting a $(G_2⋉{\mathbb{R}}^7)\times {\mathbb{R}}^2$ structure are classified.

36 pages, latex; v2, section classifying all spacetimes admitting a $(G_2⋉{\mathbb{R}}^7)\times {\mathbb{R}}^2$ structure included; v3, typos corrected. Final version to appear in Phys.Rev.D

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Cited by in corpus (15)

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• Characterization of all the supersymmetric solutions of gauged N=1,d=5 supergravity
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• New supersymmetric AdS_3 solutions
• All the supersymmetric configurations of N=4,d=4 supergravity
• Global geometry of the supersymmetric AdS_3/CFT_2 correspondence in M-theory
• Supersymmetric wrapped membranes, AdS(2) spaces, and bubbling geometries
• Supersymmetric solutions of gauged five-dimensional supergravity with general matter couplings
• The supersymmetric solutions and extensions of ungauged matter-coupled N=1,d=4 supergravity
• Null structure groups in eleven dimensions
• Invariant Killing spinors in 11D and type II supergravities
• $N=(2,0)$ AdS${}_3$ Solutions of M-theory
• On 1/2 BPS Solutions in M-theory
• Spacetime singularity resolution by M-theory fivebranes: calibrated geometry, Anti-de Sitter solutions and special holonomy metrics