Computation of generalized Killing spinors on reductive homogeneous spaces

TL;DR

This paper presents an algebraic and algorithmic method to compute the holonomy of generalized Killing spinor derivatives on pseudo-Riemannian reductive homogeneous spaces, with applications to supersymmetry in M-theory.

Contribution

It introduces a new algebraic algorithm for computing holonomy and Killing superalgebras on homogeneous spaces, applicable to supergravity and string theory models.

Findings

Computed supersymmetries of homogeneous M2 duals in M-theory

Developed an algebraic method for holonomy calculation on reductive spaces

Demonstrated the algorithm with explicit examples

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.