M-theory Compactifications on Manifolds with G2 Structure

TL;DR

This work derives the four-dimensional superpotential for M-theory compactifications on seven-manifolds with $G_2$ structure by computing the gravitino mass term, revealing a standard flux-driven piece plus a new contribution from intrinsic torsion. It then specializes to weak $G_2$ holonomy, deriving the deformation space and showing that the resulting 4D theory is an $N=1$ supergravity with $K=-3 ext{ln}oldsymbol{V}$ and a holomorphic superpotential that encodes both metric deformations and three-form moduli, with the potential matching the explicit compactification. The Freund–Rubin background is reviewed and used to connect the general $G_2$-structure analysis to concrete KK reductions, including the inclusion of internal flux and a discussion of vanishing flux cases. The results provide a coherent framework linking torsion, fluxes, and moduli in M-theory on $G_2$-structure manifolds, with implications for moduli stabilization and phenomenology in AdS$_4$ vacua.

Abstract

In this paper we study M-theory compactifications on manifolds of G2 structure. By computing the gravitino mass term in four dimensions we derive the general form for the superpotential which appears in such compactifications and show that beside the normal flux term there is a term which appears only for non-minimal G2 structure. We further apply these results to compactifications on manifolds with weak G2 holonomy and make a couple of statements regarding the deformation space of such manifolds. Finally we show that the superpotential derived from fermionic terms leads to the potential that can be derived from the explicit compactification, thus strengthening the conjectures we make about the space of deformations of manifolds with weak G2 holonomy.