Virasoro irregular conformal block and beta deformed random matrix model

TL;DR

This paper explores the connection between Virasoro irregular conformal blocks and beta-deformed matrix models, revealing modifications of Gaiotto states and explicitly verifying their relation for rank 2 cases.

Contribution

It establishes a novel representation of Virasoro irregular conformal blocks using beta-deformed matrix models and clarifies the modifications of Gaiotto states due to normalization.

Findings

Virasoro irregular conformal block expressed via Jack-polynomials

Confirmed non-trivial modifications of Gaiotto states

Explicit verification for rank 2 irregular conformal block

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.