(Weak) G2 holonomy from self-duality, flux and supersymmetry

Adel Bilal (1) , J. -P. Derendinger , Konstadinos Sfetsos (2) , Jean-Pierre Derendinger (3)

1 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]
2 Laboratory of Engineering
3 UNIBE - Universität Bern / University of Bern

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.

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Adel Bilal, J. -P. Derendinger, Konstadinos Sfetsos, Jean-Pierre Derendinger. (Weak) G2 holonomy from self-duality, flux and supersymmetry. Nuclear Physics B, 2002, 628 (1-2), pp.112-132. ⟨10.1016/S0550-3213(02)00042-1⟩. ⟨hal-02374801⟩