Matrix models for irregular conformal blocks and Argyres-Douglas theories

Abstract

As regular conformal blocks describe the N=2 superconformal gauge theories in four dimensions, irregular conformal blocks are expected to reproduce the instanton partition functions of the Argyres-Douglas theories. In this paper, we construct matrix models which reproduce the irregular conformal conformal blocks of the Liouville theory on sphere, by taking a colliding limit of the Penner-type matrix models. The resulting matrix models have not only logarithmic terms but also rational terms in the potential. We also discuss their relation to the Argyres-Douglas type theories.

42 pages, 2 figures; v2: minor corrections; v3: minor corrections, added the second paragraph in section 6

References in corpus (7)

• Matrix model version of AGT conjecture and generalized Selberg integrals
• Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
• Comments on scaling limits of 4d N=2 theories
• S-duality as a beta-deformed Fourier transform
• Generalized matrix models and AGT correspondence at all genera
• Seiberg-Witten curve via generalized matrix model
• Large N limit of beta-ensembles and deformed Seiberg-Witten relations

Cited by in corpus (29)

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• A slow review of the AGT correspondence
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• Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA
• Argyres-Douglas theories, Painlevé II and quantum mechanics
• Classical Virasoro irregular conformal block
• Virasoro irregular conformal block and beta deformed random matrix model
• Discrete Painleve system for the partition function of $N_f=2$ $SU(2)$ supersymmetric gauge theory and its double scaling limit
• Argyres-Douglas theories and Liouville Irregular States
• Classical Virasoro irregular conformal block II
• Irregular conformal block, spectral curve and flow equations
• Parametric dependence of irregular conformal block
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Multicritical points of unitary matrix model with logarithmic potential identified with Argyres-Douglas points
• On the Nekrasov Partition Function of Gauged Argyres-Douglas Theories
• Argyres-Douglas Theories, S-duality and AGT Correspondence
• Partition functions of non-Lagrangian theories from the holomorphic anomaly
• Irregular Vertex Operators for Irregular Conformal Blocks
• Irregular matrix model with $\mathcal{W}$ symmetry
• Super-spectral curve of irregular conformal blocks
• Vertex Operators for Irregular Conformal Blocks: Supersymmetric Case
• A-D hypersurface of $su(n)$ $\mathcal{N}=2$ supersymmetric gauge theory with $N_f=2n-2$ flavors
• Punctures and p-spin curves from matrix models
• Irregular Conformal States and Spectral Curve: Irregular Matrix Model Approach
• Interactions of Irregular Gaiotto States in Liouville Theory
• Higher Spins as Rolling Tachyons in Open String Field Theory
• Theory space of one unitary matrix model and its critical behavior associated with Argyres-Douglas theory