Non-Perturbative Heterotic Duals of M-Theory on $G_{2}$ Orbifolds

TL;DR

This paper explores heterotic duals of M-theory on $G_{2}$ orbifolds, revealing complex instanton configurations and duality behaviors that deepen understanding of string/M-theory compactifications.

Contribution

It provides a detailed analysis of heterotic duals to M-theory on $G_{2}$ orbifolds, including the behavior of point-like instantons and their geometric and bundle interpretations.

Findings

Identification of point-like instantons localized on orbifold loci.

Description of the 'half-G2' limit as an analog of the F-theory stable degeneration.

Insight into T-dual instanton configurations in heterotic string theory.

Abstract

By fibering the duality between the $E_{8}\times E_{8}$ heterotic string on $T^{3}$ and M-theory on K3, we study heterotic duals of M-theory compactified on $G_{2}$ orbifolds of the form $T^{7}/\mathbb{Z}_{2}^{3}$. While the heterotic compactification space is straightforward, the description of the gauge bundle is subtle, involving the physics of point-like instantons on orbifold singularities. By comparing the gauge groups of the dual theories, we deduce behavior of a "half-$G_{2}$" limit, which is the M-theory analog of the stable degeneration limit of F-theory. The heterotic backgrounds exhibit point-like instantons that are localized on pairs of orbifold loci, similar to the "gauge-locking" phenomenon seen in Ho\v{r}ava-Witten compactifications. In this way, the geometry of the $G_{2}$ orbifold is translated to bundle data in the heterotic background. While the instanton configuration looks surprising from the perspective of the $E_{8}\times E_{8}$ heterotic string, it may be understood as T-dual $\text{Spin}(32)/\mathbb{Z}_{2}$ instantons along with winding shifts originating in a dual Type I compactification.