arXiv subjects

A. Shchechkin

Publications and source records attributed to A. Shchechkin.

4 recordsLinked to original sources

arXiv2025

Refined Painlev\'e/gauge theory correspondence and quantum tau functions

In this paper we study strong coupling asymptotic expansions of $\mathcal{N}=2$ four-dimensional $SU(2)$ gauge theory partition functions in general $\Omega$-background. This is done by refining the Painlev\'e/gauge theory correspondence in terms of quantum Painlev\'e equations, obtained from $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations. We present a general ansatz and a systematic analysis of the expansions of the gauge theory partition functions by solving the above equations around the strong coupling singularities, including Argyres-Douglas points. We check our results via refined holomorphic anomaly equations and compare with irregular Virasoro conformal blocks.

hep-th↗

arXiv2021

Folding transformations for q-Painleve equations

Folding transformation of the Painlevé equations is an algebraic (of degree greater than 1) transformation between solutions of different equations. In 2005 Tsuda, Okamoto and Sakai classified folding transformations of differential Painlevé equations. These transformations are in correspondence with automorphisms of affine Dynkin diagrams. We give a complete classification of folding transformations of the $q$-difference Painlevé equations, these transformations are in correspondence with certain subdiagrams of the affine Dynkin diagrams (possibly with automorphism). The method is based on Sakai's approach to Painlevé equations through rational surfaces.

nlin.SI↗

arXiv2020

Blowup relations on $\mathbb{C}^2/\mathbb{Z}_2$ from Nakajima-Yoshioka blowup relations

We obtain bilinear relations on Nekrasov partition functions, arising from study of tau functions of quantum $q$-Painlevé equations, from Nakajima-Yoshioka blowup relations by an elementary algebraic approach. Additionaly, using this approach, we prove certain relations on Nekrasov partition functions, modified by Chern-Simons term.

math-ph↗

arXiv2019

Painleve equations from Nakajima-Yoshioka blowup relations

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.

math-ph↗