(Weak) g(2) holonomy from selfduality, flux and supersymmetry
Nov, 2001
25 pages
Published in:
- Nucl.Phys.B 628 (2002) 112-132
e-Print:
- hep-th/0111274 [hep-th]
Report number:
- NEIP-01-011
Citations per year
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 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.Note:
- references added, 25 pages, no figures, Latex Report-no: NEIP-01-011, LPTENS-01/45
- 11.25.Mj
- 11.10.Kk
- holonomy: G(2)
- duality: Spin(7)
- supersymmetry
- spinor: Killing
- differential forms
- flux
- M-theory
- supergravity
References(32)
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