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• W2076536077 abstract "For supersymmetric spacetimes in 11 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 analyzed 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 11 dimensions. The formalism is employed to show that the general bosonic solution of 11 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 ${mathrm{AdS}}_{4}$ with a seven-manifold of weak ${G}_{2}$ holonomy. In addition, all supersymmetric spacetimes admitting a $({G}_{2}ensuremath{ltimes}{mathbb{R}}^{7})ifmmodetimeselsetexttimesfi{}{mathbb{R}}^{2}$ structure are classified." @default.
• W2076536077 created "2016-06-24" @default.
• W2076536077 creator A5024606426 @default.
• W2076536077 date "2006-02-10" @default.
• W2076536077 modified "2023-09-25" @default.
• W2076536077 title "Geometry of extended null supersymmetry in M theory" @default.
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• W2076536077 doi "https://doi.org/10.1103/physrevd.73.045012" @default.
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