|Sfb 288 Differential Geometry and Quantum Physics|
Abstract for Sfb Preprint No. 589
Killing spinors in Supergravity with 4-fluxes
I. Agricola, Th. Friedrich
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 $\F \cdot \Psi = 0$ defines a non empty subfamily of solutions. We investigate the constraint $\T \cdot \Psi = 0$, too, and show that it singles out a very special choice of numerical parameters in the Killing equation, which can also be justified geometrically.
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