New G₂ metric, D6-branes and Lattice Universe

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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 R-R 2-form flux. Reducing the solution instead on the base space S¹, 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 G₂ manifold are identified with the spatial coordinates of our universe.