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

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.