Fluxes in M-theory on 7-manifolds and G structures

TL;DR

This paper studies flux compactifications of M-theory on 7-manifolds, analyzing how supersymmetry constraints affect flux configurations and the resulting geometry, especially in relation to Killing spinors and G-structures.

Contribution

It clarifies the conditions under which 4-form fluxes can be incorporated in M-theory compactifications with different numbers of Killing spinors and associated G-structures.

Findings

Single Killing spinor implies fluxes curve the external space.

Multiple Killing spinors lead to reduction to 6-manifold with SU(3) structures.

Fluxes are compatible with non-trivial SU(3) structures in certain cases.

Abstract

We consider warp compactifications of M-theory on 7-manifolds in the presence of 4-form fluxes and investigate the constraints imposed by supersymmetry. As long as the 7-manifold supports only one Killing spinor we infer from the Killing spinor equations that non-trivial 4-form fluxes will necessarily curve the external 4-dimensional space. On the other hand, if the 7-manifold has at least two Killing spinors, there is a non-trivial Killing vector yielding a reduction of the 7-manifold to a 6-manifold and we confirm that 4-form fluxes can be incorporated if one includes non-trivial SU(3) structures.