Virasoro irregular conformal block and beta deformed random matrix model

Abstract

Virasoro irregular conformal block is presented as the expectation value of Jack-polynomials of the beta-deformed Penner-type matrix model and is compared with the inner product of Gaiotto states with arbitrary rank. It is confirmed that there are non-trivial modifications of the Gaiotto states due to the normalization of the states. The relation between the two is explicitly checked for rank 2 irregular conformal block.

13 pages, 1 figure

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• Argyres-Douglas theories and Liouville Irregular States
• Classical Virasoro irregular conformal block II
• Irregular conformal block, spectral curve and flow equations
• Conformal blocks and Painlevé functions
• Irregular matrix model with $\mathcal{W}$ symmetry
• Irregular Vertex Operators for Irregular Conformal Blocks
• Nekrasov and Argyres-Douglas theories in spherical Hecke algebra representation
• Vertex Operators for Irregular Conformal Blocks: Supersymmetric Case
• Super-spectral curve of irregular conformal blocks
• Irregular Conformal States and Spectral Curve: Irregular Matrix Model Approach
• Interactions of Irregular Gaiotto States in Liouville Theory