The landscape of M-theory compactifications on seven-manifolds with G 2 holonomy

We study the physics of globally consistent four-dimensional N $$ \mathcal{N} $$ = 1 super-symmetric M-theory compactifications on G 2 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) G 2 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 G 2 manifold. We discuss physical aspects of the abelian G 2 landscape broadly, including aspects of Higgs and Coulomb branches, membrane instanton corrections, and some general aspects of topology change