Duality and Fibrations on G_2 Manifolds

TL;DR

This paper explores the structure of G_2 manifolds in M-theory, showing they can be fibered by coassociative submanifolds and connecting dual theories via M5-brane moduli spaces, with examples including K3 and torus fibrations.

Contribution

It introduces a framework linking G_2 manifolds with string dualities through fibered structures and constructs explicit examples with special fibrations and holonomy properties.

Findings

G_2 manifolds admit coassociative fibrations compatible with string dualities

Constructed explicit non-compact G_2 manifolds with K3 and torus fibrations

Kaluza-Klein reduction yields abelian BPS monopoles in 3+1 dimensions

Abstract

We argue that G_2 manifolds for M-theory admitting string theory Calabi-Yau duals are fibered by coassociative submanifolds. Dual theories are constructed using the moduli space of M5-brane fibers as target space. Mirror symmetry and various string and M-theory dualities involving G_2 manifolds may be incorporated into this framework. To give some examples, we construct two non-compact manifolds with G_2 structures: one with a K3 fibration, and one with a torus fibration and a metric of G_2 holonomy. Kaluza-Klein reduction of the latter solution gives abelian BPS monopoles in 3+1 dimensions.