Revisiting eight-manifold flux compactifications of M-theory using geometric algebra techniques

TL;DR

This paper explores M-theory flux compactifications on 8-manifolds to AdS3, using geometric algebra to analyze supersymmetry conditions with general Majorana pinors, advancing understanding of such backgrounds.

Contribution

It introduces a comprehensive analysis of supersymmetric M-theory compactifications allowing general pinors without chirality constraints, utilizing geometric algebra techniques.

Findings

Derived differential and algebraic constraints on pinor bilinears.

Lifted pinors to the 9D metric cone for analysis.

Developed efficient methods for analyzing Killing pinor equations.

Abstract

Motivated by open problems in F-theory, we reconsider warped compactifications of M theory on 8-manifolds to AdS3 spaces in the presence of a non-trivial field strength of the M-theory 3-form, studying the most general conditions under which such backgrounds preserve N=2 supersymmetry in three dimensions. In contrast with previous studies, we allow for the most general pair of Majorana generalized Killing pinors on the internal 8-manifold, without imposing any chirality conditions on those pinors. We also show how such pinors can be lifted to the 9-dimensional metric cone over the compactification 8-manifold. We describe the translation of the generalized Killing pinor equations for such backgrounds to a system of differential and algebraic constraints on certain form-valued pinor bilinears and develop techniques through which such equations can be analyzed efficiently.