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(Weak) G_2 Holonomy from Self-duality, Flux and Supersymmetry

Bilal, A, Derendinger, J-P and Sfetsos, K (2001) (Weak) G_2 Holonomy from Self-duality, Flux and Supersymmetry Nucl.Phys. B, 628. pp. 112-132.

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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 G_2 holonomy and certain generalized self-duality conditions to weak G_2 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 G_2 or weak G_2 metric.

Item Type: Article
Divisions : Surrey research (other units)
Authors :
Bilal, A
Derendinger, J-P
Date : 29 November 2001
DOI : 10.1016/S0550-3213(02)00042-1
Uncontrolled Keywords : hep-th, hep-th
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 12:26
Last Modified : 24 Jan 2020 22:15

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