The Killing spinor equation with higher order potentials

TL;DR

This paper classifies and constructs explicit solutions to supergravity spinor equations involving higher order potentials on special geometric manifolds, revealing new solutions in various dimensions.

Contribution

It introduces a classification and explicit construction of solutions to supergravity equations with higher order potentials on special geometries.

Findings

Explicit solutions on -Sasakian, almost Hermitian, and cocalibrated G_2-structures.

Solutions satisfying additional energy-momentum constraints.

New classes of solutions in dimensions 5, 6, and 7.

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 \Psi. 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 \alpha-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.