Computation of generalized Killing spinors on reductive homogeneous spaces

Abstract

We determine the holonomy of generalized Killing spinor covariant derivatives of the form $D= \nabla + \Omega$ on pseudo-Riemannian reductive homogeneous spaces in a purely algebraic and algorithmic way, where $\Omega : TM \rightarrow \Lambda^*(TM)$ is a left-invariant homomorphism. This is essentially an application of the theory of invariant principal bundle connections defined over homogeneous principal bundles. Moreover, the algorithm allows a computation of the associated Killing superalgebra in certain cases. The procedure is demonstrated by determining the supersymmetries of certain homogeneous M2 duals, which arise in M-theory.