Compact, Singular G2-Holonomy Manifolds and M/Heterotic/F-Theory Duality

TL;DR

This paper explores the duality between M-theory on G2-manifolds and heterotic string theory on Calabi-Yau three-folds, focusing on fibered G2-manifolds and their singular limits, with explicit examples and spectral checks.

Contribution

It establishes dualities for smooth and singular G2-manifolds, including non-abelian gauge groups, and provides explicit examples and spectral validations.

Findings

Dualities between M-theory on G2-manifolds and heterotic/F-theory on Calabi-Yau three-folds.

Identification of gauge groups, including non-Higgsable cases, via singular G2-manifolds.

Explicit examples demonstrating the duality and spectral consistency checks.

Abstract

We study the duality between M-theory on compact holonomy G2-manifolds and the heterotic string on Calabi-Yau three-folds. The duality is studied for K3-fibered G2-manifolds, called twisted connected sums, which lend themselves to an application of fiber-wise M-theory/Heterotic Duality. For a large class of such G2-manifolds we are able to identify the dual heterotic as well as F-theory realizations. First we establish this chain of dualities for smooth G2-manifolds. This has a natural generalization to situations with non-abelian gauge groups, which correspond to singular G2-manifolds, where each of the K3-fibers degenerates. We argue for their existence through the chain of dualities, supported by non-trivial checks of the spectra. The corresponding 4d gauge groups can be both Higgsable and non-Higgsable, and we provide several explicit examples of the general construction.