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arXiv · 2502.01499

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

G. Bonelli·A. Shchechkin·A. Tanzini
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Abstract

In this paper we study strong coupling asymptotic expansions of $\mathcal{N}=2$ four-dimensional $SU(2)$ gauge theory partition functions in general $\Omega$-background. This is done by refining the 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 check our results via refined holomorphic anomaly equations and compare with irregular Virasoro conformal blocks.

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G. Bonelli, A. Shchechkin, A. Tanzini. 2025-02-03. Refined Painlev\'e/gauge theory correspondence and quantum tau functions. https://arxiv.org/abs/2502.01499

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