Non-Abelian bundles on heterotic non-compact K3 orbifold blowups

TL;DR

This paper constructs and classifies non-Abelian gauge bundles on resolved non-compact K3 orbifolds, specifically C^2/Z_3, and compares these smooth models with orbifold limits, revealing their gauge equivalence and spectrum consistency.

Contribution

It provides explicit non-Abelian bundle examples on resolved K3 orbifolds and classifies all effective six-dimensional models with combined instantons and Abelian fluxes.

Findings

All gauge backgrounds relate to VEVs of twisted and untwisted states.

Gauge groups and spectra match between orbifold and smooth models.

Complete classification of models satisfying Bianchi constraints.

Abstract

Instantons on Eguchi-Hanson spaces provide explicit examples of stable bundles on non-compact four dimensional C^2/Z_n orbifold resolutions with non-Abelian structure groups. With this at hand, we can consider compactifications of ten dimensional SO(32) supergravity (arising as the low energy limit of the heterotic string) on the resolved spaces in the presence of non-Abelian bundles. We provide explicit examples in the resolved C^2/Z_3 case, and give a complete classification of all possible effective six dimensional models where the instantons are combined with Abelian gauge fluxes in order to fulfil the local Bianchi identity constraint. We compare these models with the corresponding C^2/Z_3 orbifold models, and find that all of these gauge backgrounds can be related to configurations of vacuum expectation values (VEV's) of twisted and sometimes untwisted states. Gauge groups and spectra are identical from both the orbifold and the smooth bundle perspectives.