Chiral Fermions from Manifolds of $G_2$ Holonomy

Abstract

M-theory compactification on a manifold X of $G_2$ holonomy can give chiral fermions in four dimensions only if X is singular. A number of examples of conical singularities that give chiral fermions are known; the present paper is devoted to describing some additional examples. In some of them, the physics can be determined but the metric is not known explicitly, while in others the metric can be described explicitly but the physics is more challenging to understand.