01308nas a2200133   4500008004100000245005300041210005000094260001300144520090800157100001601065700002001081700002201101856005101123       2014                        en  d00aN = 2 Quiver Gauge Theories on A-type ALE Spaces0 aN 2 Quiver Gauge Theories on Atype ALE Spaces  bSpringer3 aWe survey and compare recent approaches to the computation of the partition functions and correlators of chiral BPS observables in N = 2 gauge theories on ALE spaces based on quiver varieties and the minimal resolution Xk of the Ak-1 toric singularity C2/Zk, in light of their recently conjectured duality with two-dimensional coset conformal field theories. We review and elucidate the rigorous constructions of gauge theories for a particular family of ALE spaces, using their relation to the cohomology of moduli spaces of framed torsion-free sheaves on a suitable orbifold compactification of Xk. We extend these computations to generic N = 2 superconformal quiver gauge theories, obtaining in these instances new constraints on fractional instanton charges, a rigorous proof of the Nekrasov master formula, and new quantizations of Hitchin systems based on the underlying Seiberg–Witten geometry.1 aBruzzo, Ugo1 aSala, Francesco1 aSzabo, Richard J.  uhttp://urania.sissa.it/xmlui/handle/1963/34719