Geometric algebra and M-theory compactifications

TL;DR

This paper introduces a geometric algebra framework to describe supersymmetry conditions in M-theory flux compactifications, providing a unified approach with broad applications in string theory and supergravity.

Contribution

It presents a novel description of supersymmetry conditions using the Kahler-Atiyah algebra, specifically applied to M-theory compactifications on eight-manifolds preserving N=2 supersymmetry.

Findings

Supersymmetry conditions expressed via flat subalgebras of Kahler-Atiyah algebra.

Application to M-theory compactifications on eight-manifolds to AdS3 with N=2 supersymmetry.

Development of a geometric algebra approach to constrained generalized Killing pinors.

Abstract

We show how supersymmetry conditions for flux compactifications of supergravity and string theory can be described in terms of a flat subalgebra of the Kahler-Atiyah algebra of the compactification space, a description which has wide-ranging applications. As a motivating example, we consider the most general M-theory compactifications on eight-manifolds down to AdS3 spaces which preserve N=2 supersymmetry in 3 dimensions. We also give a brief sketch of the lift of such equations to the cone over the compactification space and of the geometric algebra approach to `constrained generalized Killing pinors', which forms the technical and conceptual core of our investigation.