The matrix model version of AGT conjecture and CIV-DV prepotential

Abstract

Recently exact formulas were provided for partition function of conformal (multi-Penner) beta-ensemble in the Dijkgraaf-Vafa phase, which, if interpreted as Dotsenko-Fateev correlator of screenings and analytically continued in the number of screening insertions, represents generic Virasoro conformal blocks. Actually these formulas describe the lowest terms of the q_a-expansion, where q_a parameterize the shape of the Penner potential, and are exact in the filling numbers N_a. At the same time, the older theory of CIV-DV prepotential, straightforwardly extended to arbitrary beta and to non-polynomial potentials, provides an alternative expansion: in powers of N_a and exact in q_a. We check that the two expansions coincide in the overlapping region, i.e. for the lowest terms of expansions in both q_a and N_a. This coincidence is somewhat non-trivial, since the two methods use different integration contours: integrals in one case are of the B-function (Euler-Selberg) type, while in the other case they are Gaussian integrals.

27 pages, 1 figure

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Cited by in corpus (47)

• Quantum Geometry of Refined Topological Strings
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• A direct proof of AGT conjecture at beta = 1
• Explicit examples of DIM constraints for network matrix models
• M5-branes, toric diagrams and gauge theory duality
• Seiberg-Witten theory, matrix model and AGT relation
• The uses of the refined matrix model recursion
• Matrix models for irregular conformal blocks and Argyres-Douglas theories
• Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type
• Resolvents and Seiberg-Witten representation for Gaussian beta-ensemble
• Non-Perturbative Quantum Geometry III
• A slow review of the AGT correspondence
• Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver
• Non-Perturbative Topological Strings And Conformal Blocks
• N=2 Generalized Superconformal Quiver Gauge Theory
• From Brezin-Hikami to Harer-Zagier formulas for Gaussian correlators
• Hitchin Equation, Irregular Singularity, and $N=2$ Asymptotical Free Theories
• ADE Little String Theory on a Riemann Surface (and Triality)
• Classical conformal blocks from TBA for the elliptic Calogero-Moser system
• Non-Perturbative Quantum Geometry II
• Generalized matrix models and AGT correspondence at all genera
• Non-Perturbative Quantum Geometry
• β-deformed matrix model and Nekrasov partition function
• Seiberg-Witten curve via generalized matrix model
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Triality in SU(2) Seiberg-Witten theory and Gauss hypergeometric function
• Refined matrix models from BPS counting
• Argyres-Douglas theories and Liouville Irregular States
• Comment on integrability in Dijkgraaf-Vafa beta-ensembles
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• Challenges of beta-deformation
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• The ABCDEFG of Little Strings
• Faces of matrix models
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