Superpotentials from flux compactifications of M-theory

TL;DR

This paper explores how superpotentials in M-theory flux compactifications depend on the internal manifold's structure group, analyzing cases for G_2, SU(3), and SU(2), and their implications for flux configurations.

Contribution

It provides explicit forms of superpotentials for different structure groups in M-theory flux compactifications, highlighting conditions for fluxes in each case.

Findings

G_2 structures require vanishing fluxes.

SU(3) structures involve effective 1D models.

SU(2) structures relate to Chern-Simons models.

Abstract

In flux compactifications of M-theory a superpotential is generated whose explicit form depends on the structure group of the 7-dimensional internal manifold. In this note, we discuss superpotentials for the structure groups: G_2, SU(3) or SU(2). For the G_2 case all internal fluxes have to vanish. For SU(3) structures, the non-zero flux components entering the superpotential describe an effective 1-dimensional model and a Chern-Simons model if there are SU(2) structures.