New G 2 Metric, D6-branes and Lattice Universe

We construct a new (singular) cohomogeneity-three metric of G 2 holonomy. The solution can be viewed as a triple intersection of smeared Taub-NUTs. The metric comprises three non-compact radial-type coordinate, with the principal orbits being a T 3 bundle over S 1. We consider an M-theory vacuum (Minkowski) 4 × M 7 where M 7 is the G 2 manifold. Upon reduction on a circle in the T 3 , we obtain the intersection of a D6-brane, a Taub-NUT and a 6-brane with R-R 2-form flux. Reducing the solution instead on the base space S 1 , we obtain three intersecting 6-branes all carrying R-R 2-form flux. These two configurations can be viewed as a classical flop in the type IIA string theory. After reducing on the full principal orbits and the spatial world-volume, we obtain a four-dimensional metric describing a lattice universe, in which the three non-compact coordinates of the G 2 manifold are identified with the spatial coordinates of our universe.