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

References in corpus (5)

• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems
• Asymptotically free N=2 theories and irregular conformal blocks
• A direct proof of AGT conjecture at beta = 1
• Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA
• The importance of the Selberg integral

Cited by in corpus (4)

• Conformal blocks and Painlevé functions
• Nekrasov and Argyres-Douglas theories in spherical Hecke algebra representation
• Super-spectral curve of irregular conformal blocks
• Irregular Conformal States and Spectral Curve: Irregular Matrix Model Approach