The Killing spinor equation with higher order potentials
arXiv:0707.2217 · doi:10.1016/j.geomphys.2008.05.010
Abstract
Let (M^n,g) be a Riemannian spin manifold. The basic equations in supergravity models of type IIa string theory with 4-form flux involve a 3-form T, a 4-form F, a spinorial covariant derivative \nabla depending on \nabla^g, T, F, and a \nabla-parallel spinor field Ψ. We classify and construct many explicit families of solutions to this system of spinorial field equations by means of non-integrable special geometries. The latter include α-Sasakian structures in dimensions 5 and 7, almost Hermitian structures in dimension 6 and cocalibrated G_2-structures in dimension 7. We show that there are several examples also satisfying an additional constraint for the energy-momentum tensor.
28 pages; revised, more concise
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