Symmetry Enhancements in 7d Heterotic Strings

TL;DR

This paper systematically explores the moduli space of 7-dimensional heterotic strings to identify all maximally enhanced gauge groups, revealing connections with M-theory singularity freezing and providing comprehensive data on gauge group realizations.

Contribution

It introduces a complete enumeration of gauge enhancements in 7d heterotic strings, including novel components with rank reduction and links to M-theory mechanisms.

Findings

Complete list of maximally enhanced gauge groups in 7d heterotic strings.

Identification of five components with rank reduction via holonomy.

Explicit correspondence with M-theory singularity freezing mechanism.

Abstract

We use a moduli space exploration algorithm to produce a complete list of maximally enhanced gauge groups that are realized in the heterotic string in 7d, encompassing the usual Narain component, and five other components with rank reduction realized via nontrivial holonomy triples. Using lattice embedding techniques we find an explicit match with the mechanism of singularity freezing in M-theory on K3. The complete global data for each gauge group is explicitly given.