Painleve equations from Nakajima-Yoshioka blowup relations
Mathematical Physics
2021-03-08 v2 High Energy Physics - Theory
math.MP
Exactly Solvable and Integrable Systems
Abstract
Gamayun, Iorgov and Lisovyy in 2012 proposed that tau function of the Painlev\'e equation is equal to the series of Virasoro conformal blocks. We study similar series of conformal blocks and relate it to Painlev\'e theory. The arguments are based on Nakajima-Yoshioka blowup relations on Nekrasov partition functions. We also study series of -deformed conformal blocks and relate it to -Painlev\'e equation. As an application, we prove formula for the tau function of -Painlev\'e equation.
Keywords
Cite
@article{arxiv.1811.04050,
title = {Painleve equations from Nakajima-Yoshioka blowup relations},
author = {M. Bershtein and A. Shchechkin},
journal= {arXiv preprint arXiv:1811.04050},
year = {2021}
}
Comments
v1 36 pages; v2 38 pages, many small corrections (including the title), references added