On Fractional Instanton Numbers in Six Dimensional Heterotic E8 x E8 Orbifolds

TL;DR

This paper establishes a detailed relation between level matching conditions and fractional instanton numbers in six-dimensional heterotic E8 x E8 orbifolds, providing a classification framework based on flat bundles and extending to M-theory.

Contribution

It explicitly calculates fractional instanton numbers in terms of gauge twists and links orbifold classification to flat bundle structures.

Findings

Derived the relation between level matching and fractional instanton numbers.

Explicit calculation of fractional instanton numbers from gauge twists.

Classification of orbifolds via flat bundles consistent with instanton number constraints.

Abstract

We derive the precise relation between level matching condition and fractional instanton numbers in six dimensional, abelian and supersymmetric orbifolds of E8 x E8 heterotic string theory. The fractional part of the two E8 instanton numbers is explicitly calculated in terms of the gauge twist. This relation is then used to show that the classification of these orbifolds can be given in terms of flat bundles away from the orbifold singularities under the only constraint that the sum of the fractional parts of the gauge instanton numbers match the fractional part of the gravitational instanton number locally at every fixed point. This directly carries over to M-theory on S^1/Z_2