Supersymmetry breaking, moduli stabilization, and hidden U(1) breaking in M theory

We calculate and explore the moduli potential for M theory compactified on G₂-manifolds in which the superpotential is dominated by a single membrane instanton term plus one from an asymptotically free hidden sector gauge interaction. We show that all moduli can be stabilized and that hidden sector gauge symmetries can be Higgsed at a high scale. We then compute the spectrum of superpartner masses at the grand unified theory scale and evolve it to the electroweak scale. We find a spectrum which is very similar to the G₂-minimal supersymmetric standard model with light gauginos—accessible at the LHC—and a neutral wino dark matter candidate.