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Refined Painlev\'e/gauge theory correspondence and quantum tau functions

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arxiv 2502.01499 v1 pith:PCJV7GND submitted 2025-02-03 hep-th math-phmath.MPnlin.SI

G. Bonelli , A. Shchechkin , A. Tanzini This is my paper
classification hep-thmath-phmath.MPnlin.SI
keywords gaugetheoryequationsfunctionspainlevcorrespondencecouplingexpansions
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

In this paper we study strong coupling asymptotic expansions of ${\mathcal N}=2$ $D=4$ $SU(2)$ gauge theory partition functions in general $\Omega$-background. This is done by refining Painlev\'e/gauge theory correspondence in terms of quantum Painlev\'e equations, obtained from $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations. We present a general ansatz and a systematic analysis of the expansions of the gauge theory partition functions by solving the above equations around the strong coupling singularities, including Argyres-Douglas points. We compare our results with refined holomorphic anomaly equations and irregular Virasoro conformal blocks.

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Cited by 5 Pith papers

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

  1. Degeneration limits of Virasoro vertex operators and Painlev\'e tau functions

    math-ph 2026-01 conditional novelty 7.0 of 10

    Degenerating Virasoro vertex operators yields the conjectured irregular-conformal-block expansions of the Painlevé V and IV tau functions at infinity, together with a rank r to r+1 degeneration construction.

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  4. (1,k) CFT and RH problem with the c=-2 case

    math-ph 2026-07 conditional novelty 6.0 of 10

    For (1,k) Virasoro models, periodic vertex operators plus two degenerate fields solve a modified Riemann–Hilbert problem; in the k=2, c=-2 case the solution is explicit and satisfies new bilinear identities.

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