%0 Journal Article %D 2014 %T N = 2 Quiver Gauge Theories on A-type ALE Spaces %A Ugo Bruzzo %A Francesco Sala %A Richard J. Szabo %X We 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. %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34719 %1 34918 %2 Mathematics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-10-22T12:43:35Z No. of bitstreams: 1 preprint2014.pdf: 715288 bytes, checksum: aa2d57d1d2ee3b6602bdcef73696035c (MD5) %R 10.1007/s11005-014-0734-x