D-Brane Probes of Special Holonomy Manifolds

TL;DR

This paper uses D2-brane probes to explore properties of M-theory on special holonomy manifolds, deriving gauge theories and geometric constructions related to G_2 and Spin(7) holonomy spaces.

Contribution

It introduces a G_2 quotient construction and relates gauge theory branches to the geometry of special holonomy manifolds, advancing understanding of their moduli spaces.

Findings

Derived mirror pairs of 3D N=1 gauge theories.

Realized exceptional holonomy manifolds as Coulomb and Higgs branches.

Presented a G_2 quotient construction for non-compact manifolds.

Abstract

Using D2-brane probes, we study various properties of M-theory on singular, non-compact manifolds of G_2 and Spin(7) holonomy. We derive mirror pairs of N=1 supersymmetric three-dimensional gauge theories, and apply this technique to realize exceptional holonomy manifolds as both Coulomb and Higgs branches of the D2-brane world-volume theory. We derive a ``G_2 quotient construction'' of non-compact manifolds which admit a metric of G_2 holonomy. We further discuss the moduli space of such manifolds, including the structure of geometrical transitions in each case. For completeness, we also include familiar examples of manifolds with SU(3) and Sp(2) holonomy, where some of the new ideas are clarified and tested.