G_2 Quivers

TL;DR

This paper classifies finite discrete subgroups of G_2, computes associated McKay quivers, and explores implications for M-theory gauge theories and G_2 manifold resolutions, advancing mathematical and physical understanding.

Contribution

It provides an explicit matrix classification of G_2 subgroups and derives McKay quivers, linking algebraic structures to geometric and physical theories.

Findings

Classification of finite G_2 subgroups

Explicit McKay quivers for these subgroups

Potential applications to G_2 manifold resolutions

Abstract

We present, in explicit matrix representation and a modernity befitting the community, the classification of the finite discrete subgroups of G_2 and compute the McKay quivers arising therefrom. Of physical interest are the classes of N=1 gauge theories descending from M-theory and of mathematical interest are possible steps toward a systematic study of crepant resolutions to smooth G_2 manifolds as well as generalised McKay Correspondences. This writing is a companion monograph to hep-th/9811183 and hep-th/9905212, wherein the analogues for Calabi-Yau three- and four-folds were considered.