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Virasoro irregular conformal block and beta deformed random matrix model · Around

2014

Virasoro irregular conformal block and beta deformed random matrix model

Choi, Sang Kwan, Rim, Chaiho, Zhang, Hong

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Understand

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.

Built on

R. P. Stanley, Some combinatorial properties of Jack symmetric functions,
1989
Earlier work this paper cites.
N. Seiberg and E. Witten, Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory,
1994
Earlier work this paper cites.
N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N=2 supersymmetric QCD,
1994
Earlier work this paper cites.
I. G. Macdonald, Symmetric functions and Hall polynomials,
1995
Earlier work this paper cites.
K.W.J.Kadell, An integral for the product of two Selberg-Jack symmetric functions,
1997
Earlier work this paper cites.
B. Eynard, Topological expansion for the 1-Hermitian matrix model correlation functions
2004
Earlier work this paper cites.
P. J. Forrester and S. O. Warnaar, The importance of the Selberg integral,
Original
2008
Earlier work this paper cites.

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Then

Giulio Bonelli, Kazunobu Maruyoshi, Alessandro Tanzini, Wild Quiver Gauge Theories
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2012
Later among the works it cites.
T. Nishinaka and C. Rim, Matrix models for irregular conformal blocks and Argyres-Douglas theories
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H. Kanno, K. Maruyoshi, S. Shiba, and M. Taki, W 3 irregular states and isolated N=2 superconformal field theories
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S.-K. Choi and C. Rim, Parametric dependence of irregular conformal block
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Y. Matsuo, C. Rim and H. Zhang, Construction of Gaiotto states with fundamental multiplets through Degenerate DAHA
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