@article {2014,
title = {N = 2 Quiver Gauge Theories on A-type ALE Spaces},
number = {Letters in mathematical physics;volume 105; issue 3; pages 401-445;},
year = {2014},
publisher = {Springer},
abstract = {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{\textendash}Witten geometry.},
doi = {10.1007/s11005-014-0734-x},
url = {http://urania.sissa.it/xmlui/handle/1963/34719},
author = {Ugo Bruzzo and Francesco Sala and Richard J. Szabo}
}
@article {2007,
title = {Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory},
number = {SISSA;61/2006/FM},
year = {2007},
abstract = {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.},
doi = {10.1016/j.nuclphysb.2007.02.030},
url = {http://hdl.handle.net/1963/1888},
author = {Luca Griguolo and Domenico Seminara and Richard J. Szabo and Alessandro Tanzini}
}