Generalized matrix models and AGT correspondence at all genera

Abstract

We study generalized matrix models corresponding to n-point Virasoro conformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT correspondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge theories with generalized quiver diagrams. We obtain the generalized matrix models from the perturbative evaluation of the Liouville correlation functions and verify the consistency of the description with respect to degenerations of the Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2 gauge theory as the spectral curve of the generalized matrix model, thus providing a check of AGT correspondence at all genera.

19 pages; v2: version to appear in JHEP

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Cited by in corpus (22)

• Wild Quiver Gauge Theories
• M5-branes, toric diagrams and gauge theory duality
• Seiberg-Witten theory as a Fermi gas
• Vertices, Vortices & Interacting Surface Operators
• Quantum curves for Hitchin fibrations and the Eynard-Orantin theory
• Matrix models for irregular conformal blocks and Argyres-Douglas theories
• A slow review of the AGT correspondence
• Towards a 4d/2d correspondence for Sicilian quivers
• Matrix model from N = 2 orbifold partition function
• Branes, U-folds and hyperelliptic fibrations
• β-deformed matrix model and Nekrasov partition function
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Surface defects, flavored modular differential equations and modularity
• Argyres-Douglas theories and Liouville Irregular States
• Confinement and Mayer cluster expansions
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Notes on Mayer Expansions and Matrix Models
• Notes on 3-point functions of A_{N-1} Toda theory and AGT-W relation for SU(N) quiver
• Genus one correction to Seiberg-Witten prepotential from β-deformed matrix model
• Proof of $A_n$ AGT conjecture at $\beta =1$
• 5D AGT conjecture for circular quivers