Chiral Fermions from Manifolds of $G_2$ Holonomy

TL;DR

This paper explores new examples of singular $G_2$ holonomy manifolds in M-theory compactifications that can produce chiral fermions, expanding understanding of the geometric conditions for chirality in four-dimensional theories.

Contribution

It introduces additional examples of singular $G_2$ manifolds capable of generating chiral fermions, including cases with known metrics and cases where only the physics is understood.

Findings

Examples of conical singularities producing chiral fermions are expanded.

Some manifolds have explicitly known metrics, others only their physical implications.

The study enhances the geometric understanding of chirality in M-theory compactifications.

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.