Classical Virasoro irregular conformal block

Abstract

Virasoro irregular conformal block with arbitrary rank is obtained for the classical limit or equivalently Nekrasov-Shatashvili limit using the beta-deformed irregular matrix model (Penner-type matrix model for the irregular conformal block). The same result is derived using the generalized Mathieu equation which is equivalent to the loop equation of the irregular matrix model.

18 pages; v2: comments and references added, version to appear in JHEP

References in corpus (5)

• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Asymptotically free N=2 theories and irregular conformal blocks
• On AGT Relations with Surface Operator Insertion and Stationary Limit of Beta-Ensembles
• Classical irregular block, N=2 pure gauge theory and Mathieu equation
• Virasoro irregular conformal block and beta deformed random matrix model

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• Various semiclassical limits of torus conformal blocks
• Aggregation and sedimentation of active Brownian particles at constant affinity
• Argyres-Douglas theories and Liouville Irregular States
• Classical Virasoro irregular conformal block II
• Classical limit of irregular blocks and Mathieu functions
• Finite ${\epsilon }_2$-corrections to the $\mathcal{N}=2$ SYM prepotential
• Irregular conformal block, spectral curve and flow equations
• Developments of theory of effective prepotential from extended Seiberg-Witten system and matrix models
• Classical irregular blocks, Hill's equation and PT-symmetric periodic complex potentials
• Irregular matrix model with $\mathcal{W}$ symmetry
• Classical conformal blocks, Coulomb gas integrals and Richardson-Gaudin models
• Irregular Conformal States and Spectral Curve: Irregular Matrix Model Approach