Flux, Supersymmetry and M theory on 7-manifolds

TL;DR

This paper explores the conditions for supersymmetry in M theory compactifications on 7-manifolds, showing that unwarped supersymmetric solutions require G2 holonomy and trivial flux, with extensions to include M2-branes and considerations of corrections.

Contribution

It demonstrates that unwarped supersymmetric M theory compactifications on 7-manifolds necessitate G2 holonomy and zero flux, extending Gukov's superpotential proposal to include M2-branes.

Findings

Supersymmetry requires G2 holonomy in unwarped compactifications.

Trivial warp factor and zero four-form flux are necessary for supersymmetry.

Extension of Gukov's superpotential to include M2-brane domain walls.

Abstract

Various aspects of low energy M theory compactified to four dimensions are considered. If the supersymmetry parameter is parallel in the unwarped metric, then supersymmetry requires that the warp factor is trivial, the background four-form field strength is zero and that the internal 7-manifold has $G_2$ holonomy (we assume the absence of boundaries and other impurities). A proposal of Gukov - extended here to include M2-brane domain walls - for the superpotential of the compactified theory is shown to yield the same result. Finally, we make some speculative remarks concerning higher derivative corrections and supersymmetry breaking.