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Painleve equations from Nakajima-Yoshioka blowup relations

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arxiv 1811.04050 v2 pith:RIEVP3VR submitted 2018-11-09 math-ph hep-thmath.MPnlin.SI

M. Bershtein , A. Shchechkin This is my paper
classification math-phhep-thmath.MPnlin.SI
keywords painlevblocksconformalequationseriesblowupfunctionnakajima-yoshioka
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abstract

Gamayun, Iorgov and Lisovyy in 2012 proposed that tau function of the Painlev\'e equation is equal to the series of $c=1$ Virasoro conformal blocks. We study similar series of $c=-2$ conformal blocks and relate it to Painlev\'e theory. The arguments are based on Nakajima-Yoshioka blowup relations on Nekrasov partition functions. We also study series of $q$-deformed $c=-2$ conformal blocks and relate it to $q$-Painlev\'e equation. As an application, we prove formula for the tau function of $q$-Painlev\'e $A_7^{(1)'}$ equation.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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  4. More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations

    hep-th 2026-02 conditional novelty 6.0 of 10

    For 5d N=1 pure gauge theories, Wilson-loop blowup equations can be fixed using one-form symmetry and low-instanton data, and one-instanton free energies admit a universal v=sqrt(q1q2) expansion resembling Hilbert series.

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