Irregular conformal block, spectral curve and flow equations

Abstract

Irregular conformal block is motivated by the Argyres-Douglas type of N=2 super conformal gauge theory. We investigate the classical/NS limit of the irregular conformal block using spectral curve on a Riemann surface with irregular punctures, which is equivalent to the loop equation of irregular matrix model. The spectral curve is reduced to the second order (Virasoro symmetry, $SU(2)$ for the gauge theory) and third order ($W_3$ symmetry, $SU(3)$) differential equations of a polynomial with finite degree. The Virasoro and W symmetry generate flow equations in the spectral curve and determine the irregular conformal block, hence the partition function of the Argyres-Douglas theory ala AGT conjecture.

35 pages; v2: 38 pages, section 4 and references added, minor changes

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Cited by in corpus (11)

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• Argyres-Douglas Theories, S-duality and AGT Correspondence
• Irregular Vertex Operators for Irregular Conformal Blocks
• Nekrasov and Argyres-Douglas theories in spherical Hecke algebra representation
• Super-spectral curve of irregular conformal blocks
• Vertex Operators for Irregular Conformal Blocks: Supersymmetric Case
• Connection formulae in the Collision Limit I: Case Studies in Lifshitz Geometry
• Deformed SW curve and the null vector decoupling equation in Toda field theory
• Irregular Conformal States and Spectral Curve: Irregular Matrix Model Approach