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Mathematical Physics

arXiv:1811.04050 (math-ph)
[Submitted on 9 Nov 2018 (v1), last revised 12 Aug 2019 (this version, v2)]

Title:Painleve equations from Nakajima-Yoshioka blowup relations

Authors:M. Bershtein, A. Shchechkin
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Abstract:Gamayun, Iorgov and Lisovyy in 2012 proposed that tau function of the Painlevé 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 Painlevé 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 $q$-Painlevé equation. As an application, we prove formula for the tau function of $q$-Painlevé $A_7^{(1)'}$ equation.
Comments: v1 36 pages; v2 38 pages, many small corrections (including the title), references added
Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Exactly Solvable and Integrable Systems (nlin.SI)
Cite as: arXiv:1811.04050 [math-ph]
  (or arXiv:1811.04050v2 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1811.04050
Journal reference: Lett Math Phys 109, 2359-2402 (2019)
Related DOI: https://doi.org/10.1007/s11005-019-01198-4

Submission history

From: Anton Shchechkin [view email]
[v1] Fri, 9 Nov 2018 18:09:22 UTC (39 KB)
[v2] Mon, 12 Aug 2019 12:36:02 UTC (42 KB)
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