Merging Heterotic Orbifolds and K3 Compactifications with Line Bundles

TL;DR

This paper explores the correspondence between heterotic orbifold compactifications and smooth K3 compactifications with line bundles, providing detailed classifications and matching conditions for various orbifold cases.

Contribution

It systematically analyzes the relation between orbifold and smooth heterotic K3 compactifications, including explicit examples and conditions for line bundle matchings.

Findings

Complete classification for T^4/Z_2 and Z_3 cases.

Partial matchings for T^4/Z_4 and Z_6 cases.

Identification of conditions for single and multiple line bundle matchings.

Abstract

We clarify the relation between six-dimensional Abelian orbifold compactifications of the heterotic string and smooth heterotic K3 compactifications with line bundles for both SO(32) and E_8 x E_8 gauge groups. The T^4/Z_N cases for N=2,3,4 are treated exhaustively, and for N=6 some examples are given. While all T^4/Z_2 and nearly all T^4/Z_3 models have a simple smooth match involving one line bundle only, this is only true for some T^4/Z_4 and T^4/Z_6 cases. We comment on possible matchings with more than one line bundle for the remaining cases. The matching is provided by comparisons of the massless spectra and their anomalies as well as a field theoretic analysis of the blow-ups.