%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 Seibergâ€“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
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%R 10.1007/s11005-014-0734-x
%0 Report
%D 2007
%T Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
%A Luca Griguolo
%A Domenico Seminara
%A Richard J. Szabo
%A Alessandro Tanzini
%X We study the relationship between instanton counting in N=4 Yang-Mills theory on a generic four-dimensional toric orbifold and the semi-classical expansion of q-deformed Yang-Mills theory on the blowups of the minimal resolution of the orbifold singularity, with an eye to clarifying the recent proposal of using two-dimensional gauge theories to count microstates of black holes in four dimensions. We describe explicitly the instanton contributions to the counting of D-brane bound states which are captured by the two-dimensional gauge theory. We derive an intimate relationship between the two-dimensional Yang-Mills theory and Chern-Simons theory on generic Lens spaces, and use it to show that the correct instanton counting is only reproduced when the Chern-Simons contributions are treated as non-dynamical boundary conditions in the D4-brane gauge theory. We also use this correspondence to discuss the counting of instantons on higher genus ruled Riemann surfaces.
%B Nucl. Phys. B 772 (2007) 1-24
%G en_US
%U http://hdl.handle.net/1963/1888
%1 2347
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2006-11-09T10:57:35Z\\nNo. of bitstreams: 1\\nhep-th0610155.pdf: 340757 bytes, checksum: fb3e5bfec5e2a4c15d97a9ca6f2e8a0a (MD5)
%R 10.1016/j.nuclphysb.2007.02.030