TY - JOUR
T1 - N = 2 Quiver Gauge Theories on A-type ALE Spaces
Y1 - 2014
A1 - Ugo Bruzzo
A1 - Francesco Sala
A1 - Richard J. Szabo
AB - 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.
PB - Springer
UR - http://urania.sissa.it/xmlui/handle/1963/34719
U1 - 34918
U2 - Mathematics
U4 - 1
ER -
TY - RPRT
T1 - Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
Y1 - 2007
A1 - Luca Griguolo
A1 - Domenico Seminara
A1 - Richard J. Szabo
A1 - Alessandro Tanzini
AB - 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.
JF - Nucl. Phys. B 772 (2007) 1-24
UR - http://hdl.handle.net/1963/1888
U1 - 2347
U2 - Mathematics
U3 - Mathematical Physics
ER -