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• W2005188844 abstract "The aim of this paper is two-fold. First, we provide a simple and pedagogical discussion of how compactifications of M-theory or supergravity preserving some four-dimensional supersymmetry naturally lead to reduced holonomy or its generalization, reduced weak holonomy. We relate the existence of a (conformal) Killing spinor to the existence of certain closed and co-closed p-forms, and to the metric being Ricci flat or Einstein. Then, for seven-dimensional manifolds, we show that octonionic self-duality conditions on the spin connection are equivalent to G2 holonomy and certain generalized self-duality conditions to weak G2 holonomy. The latter lift to self-duality conditions for cohomogeneity-one spin(7) metrics. To illustrate the power of this approach, we present several examples where the self-duality condition largely simplifies the derivation of a G2 or weak G2 metric." @default.
• W2005188844 created "2016-06-24" @default.
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• W2005188844 date "2002-04-01" @default.
• W2005188844 modified "2023-10-16" @default.
• W2005188844 title "(Weak) G2 holonomy from self-duality, flux and supersymmetry" @default.
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• W2005188844 doi "https://doi.org/10.1016/s0550-3213(02)00042-1" @default.
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