Seiberg-Witten theory, matrix model and AGT relation

Abstract

We discuss the Penner-type matrix model which has been proposed to explain the AGT relation between the 2-dimensional Liouville theory and 4-dimensional N=2 superconformal gauge theories. In our previous communication we have obtained the spectral curve of the matrix model and showed that it agrees with that derived from M-theory. We have also discussed the decoupling limit of massive flavors and proposed new matrix models which describe Seiberg-Witten theory with flavors N_f=2,3. In this article we explicitly evaluate the free energy of these matrix models and show that they in fact reproduce the amplitudes of Seiberg-Witten theory.

19 pages, 1 figure

References in corpus (2)

• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Matrix model version of AGT conjecture and generalized Selberg integrals

Cited by in corpus (73)

• Wild Quiver Gauge Theories
• Deformed Prepotential, Quantum Integrable System and Liouville Field Theory
• Proving AGT conjecture as HS duality: extension to five dimensions
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Superpolynomials for toric knots from evolution induced by cut-and-join operators
• On KP-integrable Hurwitz functions
• A direct proof of AGT conjecture at beta = 1
• Ding-Iohara-Miki symmetry of network matrix models
• Explicit examples of DIM constraints for network matrix models
• M5-branes, toric diagrams and gauge theory duality
• Seiberg-Witten theory as a Fermi gas
• On the complete perturbative solution of one-matrix models
• $(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
• Towards a proof of AGT conjecture by methods of matrix models
• AGT conjecture and Integrable structure of Conformal field theory for c=1
• Brezin-Gross-Witten model as "pure gauge" limit of Selberg integrals
• Delayed Deconfinement and the Hawking-Page Transition
• Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• Matrix models for irregular conformal blocks and Argyres-Douglas theories
• Resolvents and Seiberg-Witten representation for Gaussian beta-ensemble
• Holomorphic blocks and the 5d AGT correspondence
• A slow review of the AGT correspondence
• Analysis of correlation functions in Toda theory and AGT-W relation for SU(3) quiver
• S-duality as a beta-deformed Fourier transform
• Generalized Macdonald polynomials, spectral duality for conformal blocks and AGT correspondence in five dimensions
• Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings
• Non-Perturbative Topological Strings And Conformal Blocks
• N=2 Generalized Superconformal Quiver Gauge Theory
• On elementary proof of AGT relations from six dimensions
• Torus HOMFLY as the Hall-Littlewood Polynomials
• Quantum Hitchin Systems via beta-deformed Matrix Models
• Classical conformal blocks from TBA for the elliptic Calogero-Moser system
• Matrix model from N = 2 orbifold partition function
• Generalized matrix models and AGT correspondence at all genera
• On determinant representation and integrability of Nekrasov functions
• S-Duality and Modular Transformation as a non-perturbative deformation of the ordinary pq-duality
• S-duality as Fourier transform for arbitrary ${\epsilon }_1,{\epsilon }_2$
• W(1+infinity) algebra as a symmetry behind AGT relation
• Seiberg-Witten curve via generalized matrix model
• β-deformed matrix model and Nekrasov partition function
• Complex saddles in the Gross-Witten-Wadia matrix model
• Complete solution to Gaussian tensor model and its integrable properties
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
• Seiberg-Witten curves and double-elliptic integrable systems
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations
• Uniformization, Calogero-Moser/Heun duality and Sutherland/bubbling pants
• Discrete Painleve system and the double scaling limit of the matrix model for irregular conformal block and gauge theory
• Superintegrability as the hidden origin of Nekrasov calculus
• Large N techniques for Nekrasov partition functions and AGT conjecture
• Argyres-Douglas theories and Liouville Irregular States
• Discrete Painleve system for the partition function of $N_f=2$ $SU(2)$ supersymmetric gauge theory and its double scaling limit
• Comment on integrability in Dijkgraaf-Vafa beta-ensembles
• Non-perturbative studies of N=2 conformal quiver gauge theories
• Irregular conformal block, spectral curve and flow equations
• Matching branches of non-perturbative conformal block at its singularity divisor
• Orthogonal Polynomials in Mathematical Physics
• Challenges of beta-deformation
• q-Painleve equation from Virasoro constraints
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Check-Operators and Quantum Spectral Curves
• Elliptic $q,t$ matrix models
• On generalized Macdonald polynomials
• N=2 supersymmetric QCD and elliptic potentials
• Faces of matrix models
• Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories
• Penner Type Ensemble for Gauge Theories Revisited
• Quantum spectral curve for (q,t)-matrix model
• Note on refined topological vertex, Jack polynomials and instanton counting
• Genus one correction to Seiberg-Witten prepotential from β-deformed matrix model
• Discrete Painleve equation, Miwa variables, and string equation in 5d matrix models
• Geometric transitions, double scaling limits and gauge theories
• Theory space of one unitary matrix model and its critical behavior associated with Argyres-Douglas theory