Painlevé equations from NakajimaYoshioka blowup relations
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 NakajimaYoshioka blowup relations on Nekrasov partition functions. We also study series of qdeformed c=2 conformal blocks and relate it to qPainlevé equation. As an application, we prove formula for the tau function of qPainlevé A_7^{(1)'} equation.
 Publication:

Letters in Mathematical Physics
 Pub Date:
 November 2019
 DOI:
 10.1007/s11005019011984
 arXiv:
 arXiv:1811.04050
 Bibcode:
 2019LMaPh.109.2359B
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 v1 36 pages