Journal of High Energy Physics, v.(6), no., pp.054-1 - 054-47
We study constrained generalized Killing spinors over the metric cone and
cylinder of a (pseudo-)Riemannian manifold, developing a toolkit which can be used to investigate
certain problems arising in supersymmetric flux compactifications of supergravity
theories. Using geometric algebra techniques, we give conceptually clear and computationally
effective methods for translating supersymmetry conditions for the metric and fluxes
of the unit section of such cylinders and cones into differential and algebraic constraints
on collections of differential forms defined on the cylinder or cone. In particular, we give
a synthetic description of Fierz identities, which are an important ingredient of such problems.
As a non-trivial application, we consider the most general N = 2 compactification
of eleven-dimensional supergravity on eight-manifolds.