M-theory Compactifications on Manifolds with G2 Structure

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.Comment: 34 pages. Minor changes: typos corrected, references added. Version to appear in Class. Quantum Gra