Matter From G(2) Manifolds

TL;DR

This paper explores how chiral matter arises from G(2) holonomy manifolds in M-theory compactifications, linking geometric singularities to gauge theories and matter representations, including exotic cases relevant for grand unification.

Contribution

It provides a geometric description of matter from G(2) manifolds, including explicit metrics and connections to type IIA D-brane configurations with novel matter representations.

Findings

Chiral matter arises from codimension seven singularities in G(2) manifolds.

Explicit G(2) metrics are constructed in certain cases.

Inclusion of orientifold planes yields exotic matter representations.

Abstract

We describe how chiral matter charged under SU(N) and SO(2N) gauge groups arises from codimension seven singularities in compactifications of M-theory on manifolds with G(2) holonomy. The geometry of these spaces is that of a cone over a six-dimensional Einstein space which can be constructed by (multiple) unfolding of hyper-Kahler quotient spaces. In type IIA the corresponding picture is given by stacks of intersecting D6-branes and chiral matter arises from open strings stretching between them. Usually one obtains (bi)fundamental representations but by including orientifold six-planes in the type IIA picture we find more exotic representations like the anti-symmetric, which is important for the study of SU(5) grand unification, and trifundamental representations. We also exhibit many cases where the G(2) metrics can be described explicitly, although in general the metrics on the spaces constructed via unfolding are not known.