Multi instanton calculus on ALE spaces

Abstract

We study SYM gauge theories living on ALE spaces. Using localization formulae we compute the prepotential (and its gravitational corrections) for SU(N) supersymmetric $\mathcal{N}=2,2^{\ast }$ gauge theories on ALE spaces of the $A_n$ type. Furthermore we derive the Poincaré polynomial describing the homologies of the corresponding moduli spaces of self-dual gauge connections. From these results we extract the $\mathcal{N}=4$ partition function which is a modular form in agreement with the expectations of $SL(2,\mathbb{Z})$ duality.

26 pages, few explanations added. version to appear in nucl.phys

References in corpus (3)

• Small Instantons, Little Strings and Free Fermions
• Seiberg-Witten Theory and Random Partitions
• Instantons on Quivers and Orientifolds

Cited by in corpus (71)

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• Deformed N=2 theories, generalized recursion relations and S-duality
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
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• Topological strings and large N phase transitions II: Chiral expansion of q-deformed Yang-Mills theory
• Instantons on ALE spaces and orbifold partitions
• Parafermionic Liouville field theory and instantons on ALE spaces
• 2d-4d Connection between q-Virasoro/W Block at Root of Unity Limit and Instanton Partition Function on ALE Space
• Coset conformal blocks and N=2 gauge theories
• N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae
• Hilbert Series for Moduli Spaces of Instantons on C^2/Z_n
• Topological strings and large N phase transitions I: Nonchiral expansion of q-deformed Yang-Mills theory
• A Combinatorial Study on Quiver Varieties
• Matrix model from N = 2 orbifold partition function
• Scheme dependence of instanton counting in ALE spaces
• On 't Hooft Defects, Monopole Bubbling and Supersymmetric Quantum Mechanics
• Poincare polynomial of moduli spaces of framed sheaves on (stacky) Hirzebruch surfaces
• The moduli space of instantons on an ALE space from 3d $\mathcal{N}=4$ field theories
• A brief review of the 2d/4d correspondences
• Amoebas and Instantons
• Black-holes, topological strings and large N phase transitions
• Instanton on toric singularities and black hole countings
• Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities
• N=2 quiver gauge theories on A-type ALE spaces
• Coset conformal field theory and instanton counting on C^2/Z_p
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• S-duality, triangle groups and modular anomalies in N=2 SQCD
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• N=2 gauge theories, instanton moduli spaces and geometric representation theory
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
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• N=2 superconformal blocks and instanton partition functions
• Gauge theories on compact toric manifolds
• Moduli spaces of SO(8) instantons on smooth ALE spaces as Higgs branches of 4d N=2 supersymmetric theories
• Exact partition functions for the $\Omega$-deformed $\mathcal{N}=2^{\ast }$ $SU(2)$ gauge theory
• Modular anomaly equations and S-duality in N=2 conformal SQCD
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• Holomorphic Anomaly in Gauge Theory on ALE space
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• Noncommutative Instantons in Diverse Dimensions
• Resumming instantons in N=2* theories with arbitrary gauge groups
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• Super Topological Recursion and Gaiotto Vectors For Superconformal Blocks
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• $n$-th parafermion ${\mathcal{W}}_N$ characters from $U(N)$ instanton counting on ${\mathbb{C}}^2/{\mathbb{Z}}_n$
• Orbifold Vortex and Super Liouville Theory
• The ADHM-like Constructions for Instantons on CP^2 and Three Dimensional Gauge Theories
• The light asymptotic limit of conformal blocks in $\mathcal{N}=1$ super Liouville field theory
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• Notes On U(1) Instanton Counting On $A_{l-1}$ ALE Spaces