New G_2 metric, D6-branes and Lattice Universe

TL;DR

This paper constructs a new G_2 holonomy metric related to intersecting branes, leading to a lattice universe model in four-dimensional spacetime with potential implications for string theory and cosmology.

Contribution

It introduces a novel singular G_2 metric with a triple intersection structure and explores its reductions, resulting in a lattice universe model within M-theory and string theory frameworks.

Findings

New G_2 metric with triple intersection structure

Reduction yields intersecting D6-branes with flux

Lattice universe model in four dimensions

Abstract

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 coordinates, with the principal orbits being a T^3 bundle over S^1. We consider an M-theory vacuum (Minkowski)_4\times 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.