Matter From G(2) Manifolds

TL;DR

The paper constructs a broad framework for generating chiral matter in four-dimensional theories from M-theory compactifications on $G_2$ manifolds by unfolding hyper-Kähler quotient singularities. It connects these geometries to Type IIA setups with intersecting D6-branes and orientifolds, enabling chiral representations such as bifundamentals, antisymmetrics, and trifundamentals, including realizations for $D_n$ and exceptional $E_6$/$E_7$ groups. It also clarifies the relation between unfolding and twistor-space constructions, identifying cases where explicit $G_2$ metrics are available. The work underscores both the utility of these unfoldings for model-building and the need for more explicit metrics, especially in the general, non-twistor cases and for compact $G_2$ manifolds.

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.