New G2 metric, D6-branes and lattice universe Original Research Article

We construct a new (singular) cohomogeneity-three metric of G2 holonomy. The solution can be viewed as a triple intersection of smeared Taub–NUTs. The metric comprises three non-compact radial-type coordinates, with the principal orbits being a T3 bundle over S1. We consider an M-theory vacuum (Minkowski)4×M7 where M7 is the G2 manifold. Upon reduction on a circle in the T3, we obtain the intersection of a D6-brane, a Taub–NUT and a 6-brane with RR 2-form flux. Reducing the solution instead on the base space S1, we obtain three intersecting 6-branes all carrying RR 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 G2 manifold are identified with the spatial coordinates of our universe.