KZ connections with irregular singularities have monodromies that realize topological invariants of links and tangles.
Virasoro irregular conformal block and beta deformed random matrix model
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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.
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On the monodromy of KZ-connections with irregular singularities
KZ connections with irregular singularities have monodromies that realize topological invariants of links and tangles.