Classification of supersymmetric spacetimes in eleven dimensions

Abstract

We derive, for spacetimes admitting a Spin(7) structure, the general local bosonic solution of the Killing spinor equation of eleven dimensional supergravity. The metric, four form and Killing spinors are determined explicitly, up to an arbitrary eight-manifold of Spin(7) holonomy. It is sufficient to impose the Bianchi identity and one particular component of the four form field equation to ensure that the solution of the Killing spinor equation also satisfies all the field equations, and we give these conditions explicitly.

arXiv comment9 pages, latex. v2: change of title (formerly known as "Spin(7) structures in eleven dimensions"); short section on integrability conditions added, various minor changes. To appear in Phys.Rev.Lett

References in corpus (7)

• The Geometry of D=11 Killing Spinors
• G-Structures and Wrapped NS5-Branes
• The Geometry of D=11 Null Killing Spinors
• The spinorial geometry of supersymmetric backgrounds
• Brane Resolution Through Transgression
• Refining G-structure classifications
• Null structure groups in eleven dimensions

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• Null structure groups in eleven dimensions
• The geometry of extended null supersymmetry in M-theory
• Eight-manifolds with G-structure in eleven dimensional supergravity
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• Spinorial Geometry and Supergravity