The landscape of M-theory compactifications on seven-manifolds with G2 holonomy

We study the physics of globally consistent four-dimensional N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{document} = 1 super-symmetric M-theory compactifications on G2 manifolds constructed via twisted connected sum; there are now perhaps fifty million examples of these manifolds. We study a rich example that exhibits U(1)3 gauge symmetry and a spectrum of massive charged particles that includes a trifundamental. Applying recent mathematical results to this example, we compute the form of membrane instanton corrections to the superpotential and spacetime topology change in a compact model; the latter include both the (non-isolated) G2 flop and conifold transitions. The conifold transition spontaneously breaks the gauge symmetry to U(1)2, and associated field theoretic computations of particle charges make correct predictions for the topology of the deformed G2 manifold. We discuss physical aspects of the abelian G2 landscape broadly, including aspects of Higgs and Coulomb branches, membrane instanton corrections, and some general aspects of topology change.