Supersymmetric M-theory compactifications with fluxes on seven-manifolds and G-structures

TL;DR

This paper investigates supersymmetric Minkowski compactifications of M-theory on seven-manifolds with fluxes, establishing relations between flux components and manifold torsion, and exploring conditions for N=1 and N=2 supersymmetry.

Contribution

It derives conditions linking four-form flux components to the intrinsic torsion of seven-manifolds with G_2 structure, advancing understanding of flux compactifications in M-theory.

Findings

Relations between flux components and torsion for supersymmetry

Existence of two nowhere vanishing vectors on G_2 manifolds

Conditions for N=1 and N=2 supersymmetric compactifications

Abstract

We consider Minkowski compactifications of M-theory on generic seven-dimensional manifolds. After analyzing the conditions on the four-form flux, we establish a set of relations between the components of the intrinsic torsion of the internal manifold and the components of the four-form flux needed for preserving supersymmetry. The existence of two nowhere vanishing vectors on any seven-manifold with G_2 structure plays a crucial role in our analysis, leading to the possibility of four-dimensional compactifications with N=1 and N=2 supersymmetry.