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A note on rank 5/2 Liouville irregular block, Painlev\'e 1 and the {cal H}₀ Argyres-Douglas theory

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arxiv 2308.09623 v3 pith:Y3SF46TS submitted 2023-08-18 hep-th

A note on rank 5/2 Liouville irregular block, Painlev\'e 1 and the ${\cal H}_0$ Argyres-Douglas theory

classification hep-th
keywords epsilonargyres-douglasbackgroundirregularliouvilleomegaorderpainlev
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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abstract

We study 4d type ${\cal H}_0$ Argyres-Douglas theory in $\Omega$-background by constructing Liouville irregular state of rank 5/2. The results are compared with generalized Holomorphic anomaly approach, which provides order by order expansion in $\Omega$-background parameters $\epsilon_{1,2}$. Another crucial test of our results provides comparison with respect to Painlev\'{e} 1 $\tau$-function, which was expected to be hold in self-dual case $\epsilon_1=-\epsilon_2$. We also discuss Nekrasov-Shatashvili limit $\epsilon_1=0$, accessible either by means of deformed Seiberg-Witten curve, or WKB methods.

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Cited by 2 Pith papers

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

  1. Accessory Parameter of Confluent Heun Equations, Voros Periods and classical irregular conformal blocks

    math-ph 2026-05 unverdicted novelty 6.0

    Formal series expansions of accessory parameters in confluent Heun equations are obtained from Voros periods and matched to classical irregular conformal blocks by choosing appropriate cycles on the spectral curve.

  2. Les Houches Lectures on Exact WKB Analysis and Painlev\'e Equations

    math-ph 2025-12 unverdicted novelty 3.0

    Lecture notes review exact WKB analysis for ODEs and its combination with topological recursion and isomonodromy to compute monodromy and resurgent structures for Painlevé equations.