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 $\Omega :TM\to {\Lambda }^{\ast }(TM)$ 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.

9 pages