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Title:
BPZ equation and Riemann-Hilbert correspondence from gauge theory
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Abstract:
We study linear quiver theories in 4d at special values of masses. We show that the partition function of such a theory of A_1-type obeys the Belavin-Polyakov-Zamolodchikov equation. In the limit e2 -> 0 this equation becomes the eigenproblem of the generalized Heun operator. In the limit e1 -> 0 this equation becomes the Painleve VI and its multi-point generalizations. As a by-product we prove the conjecture of Nekrasov-Rosly-Shatashvili relating the generating function of SL(2) opers in genus zero to the effective twisted superpotential of the A_1-type linear quiver theory.
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