Killing spinors in supergravity with 4-fluxes

Abstract

We study the spinorial Killing equation of supergravity involving a torsion 3-form $\T$ as well as a flux 4-form $\F$. In dimension seven, we construct explicit families of compact solutions out of 3-Sasakian geometries, nearly parallel $\G_2$-geometries and on the homogeneous Aloff-Wallach space. The constraint $\F \cdot Ψ= 0$ defines a non empty subfamily of solutions. We investigate the constraint $\T \cdot Ψ= 0$, too, and show that it singles out a very special choice of numerical parameters in the Killing equation, which can also be justified geometrically.

References in corpus (1)

• Fluxes in M-theory on 7-manifolds and G structures

Cited by in corpus (7)

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• Hidden Symmetries of Euclideanised Kerr-NUT-(A)dS Metrics in Certain Scaling Limits
• G2-structures for N=1 supersymmetric AdS4 solutions of M-theory
• Decomposable $(4,7)$ solutions in eleven-dimensional supergravity
• The Killing spinor equation with higher order potentials