Geometric algebra techniques in flux compactifications

TL;DR

This paper introduces geometric algebra methods to analyze supersymmetric flux compactifications in supergravity, providing clear computational tools and applying them to M-theory on eight-manifolds.

Contribution

It develops a geometric algebra framework for translating supersymmetry conditions into differential form constraints, enhancing computational efficiency and conceptual clarity.

Findings

Efficient recovery of N=1 M-theory compactification results

Synthetic description of Fierz identities

New computational techniques for supersymmetry conditions

Abstract

We study `constrained generalized Killing (s)pinors', which characterize supersymmetric flux compactifications of supergravity theories. Using geometric algebra techniques, we give conceptually clear and computationally effective methods for translating supersymmetry conditions into differential and algebraic constraints on collections of differential forms. In particular, we give a synthetic description of Fierz identities, which are an important ingredient of such problems. As an application, we show how our approach can be used to efficiently recover results pertaining to N=1 compactifications of M-theory on eight-manifolds.