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 $X_k$ of the $A_{k-1}$ toric singularity $\C^2/\Z_k$, 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 $X_k$. 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.

N=2 quiver gauge theories on A-type ALE spaces / Bruzzo, Ugo; Sala, Francesco; Szabo, R. J.. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 105:3(2015), pp. 401-445. [10.1007/s11005-014-0734-x]

N=2 quiver gauge theories on A-type ALE spaces

Bruzzo, Ugo
;
Sala, Francesco;
2015-01-01

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 $X_k$ of the $A_{k-1}$ toric singularity $\C^2/\Z_k$, 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 $X_k$. 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.
2015
105
3
401
445
https://arxiv.org/abs/1410.2742
Bruzzo, Ugo; Sala, Francesco; Szabo, R. J.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/11387
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