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 A7(1)′ equation.
Painlevé equations from Nakajima–Yoshioka blowup relations / Bershtein, M.; Shchechkin, A.. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 109:11(2019), pp. 2359-2402. [10.1007/s11005-019-01198-4]
Painlevé equations from Nakajima–Yoshioka blowup relations
Bershtein M.;Shchechkin A.
2019-01-01
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 A7(1)′ equation.| File | Dimensione | Formato | |
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