Heterotic orbifolds, reduced rank and SO(2n+1) characters

TL;DR

This paper develops a unified approach to describing moduli space components of heterotic strings with SO(2n+1) gauge symmetry, using affine characters and free-orbifold models, revealing novel orbifold structures and gauge configurations.

Contribution

It introduces a method to describe continuous Wilson lines and discrete deformations in heterotic string moduli space with SO(2n+1) factors, using affine SO(2n+1) characters and orbifold models.

Findings

All backgrounds can be described by free-orbifold models.

Orbifold generators act symmetrically or asymmetrically with or without discrete torsion.

A new orbifold description of 10D heterotic string with gauge degrees as twisted states.

Abstract

The moduli space of the maximally supersymmetric heterotic string in d-dimensional Minkowski space contains various components characterized by the rank of the gauge symmetries of the vacua they parametrize. We develop an approach for describing in a unified way continuous Wilson lines which parametrize a component of the moduli space, together with discrete deformations responsible for the switch from one component to the other. Applied to a component that contains vacua with SO(2n+1) gauge-symmetry factors, our approach yields a description of all backgrounds of the component in terms of free-orbifold models. The orbifold generators turn out to act symmetrically or asymmetrically on the internal space, with or without discrete torsion. Our derivations use extensively affine characters of SO(2n+1). As a by-product, we find a peculiar orbifold description of the heterotic string in ten dimensions, where all gauge degrees of freedom arise as twisted states, while the untwisted sector reduces to the gravitational degrees of freedom.