Foliated backgrounds for M-theory compactifications (I)

TL;DR

This paper characterizes eight-dimensional internal manifolds in M-theory flux compactifications to AdS3, focusing on their geometric and topological structures under supersymmetry constraints, especially non-chiral internal spinors.

Contribution

It provides a rigorous geometric and topological description of internal manifolds with specific foliation and G2 structures in M-theory compactifications.

Findings

Characterization of internal manifolds via codimension one foliation.

Identification of leafwise G2 structure on the foliation.

Rigorous topological and geometric classification of these manifolds.

Abstract

We summarize our geometric and topological description of compact eight-manifolds which arise as internal spaces in ${\cal N}=1$ flux compactifications of M-theory down to $\mathrm{AdS}_3$, under the assumption that the internal part of the supersymmetry generator is everywhere non-chiral. Specifying such a supersymmetric background is {\em equivalent} with giving a certain codimension one foliation defined by a closed one-form and which carries a leafwise $G_2$ structure, a foliation whose topology and geometry we characterize rigorously.