On Fractional Instanton Numbers in Six Dimensional Heterotic E_8 x E_8 Orbifolds

TL;DR

This paper explores how fractional instanton numbers relate to level matching in six-dimensional heterotic E_8 x E_8 orbifolds, providing a new classification approach and implications for Kaluza-Klein monopoles.

Contribution

It introduces an equivalence between level matching conditions and fractional instanton numbers, offering a novel classification method for heterotic orbifolds.

Findings

Fractional gauge and gravitational instanton numbers characterize level matching.

Classification of orbifolds can be reformulated via flat bundles.

Applications to heterotic string Kaluza-Klein monopoles.

Abstract

We show how the level matching condition in six dimensional, abelian and supersymmetric orbifolds of the E_8 x E_8 heterotic string can be given equivalently in terms of fractional gauge and gravitational instanton numbers. This relation is used to restate the classification of the orbifolds in terms of flat bundles away from the orbifold singularities under the constraint of the level matching condition. In an outlook these results are applied to Kaluza-Klein monopoles of the heterotic string on S^1 in Wilson line backgrounds.