arXiv subjects

Anton Shchechkin

Publications and source records attributed to Anton Shchechkin.

3 recordsLinked to original sources

arXiv2026

(1,k) CFT and RH problem with the c=-2 case

Following approach of Iorgov--Lisovyy--Teschner, we construct solutions of the (modified) Riemann--Hilbert problem using conformal blocks of $(1,k)$ Virasoro models. For $k>1$ case, the solution of this Riemann--Hilbert problem is not unique due to more singular behavior at punctures. On the CFT side the dimension of the space of conformal blocks also increases. We specifically study the $k=2$ case, which corresponds to the central charge $c=-2$ and symplectic fermions. We explicitly construct a corresponding solution of the modified Riemann--Hilbert problem in the case of 3 punctures and prove its uniqueness under suitable initial data conditions. We also obtain new bilinear relations for $c=-2$ tau functions.

math-ph↗

arXiv2025

Bilinear tau forms of quantum Painlev\'e equations and $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations in SUSY gauge theories

We derive bilinear tau forms of the canonically quantized Painlev\'e equations, thereby relating them to those previously obtained from the $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations for the $\mathcal{N}=2$ supersymmetric gauge theory partition functions on a general $\Omega$-background. We fully fix the refined Painlev\'e/gauge theory dictionary by formulating the proper equations for the quantum nonautonomous Painlev\'e Hamiltonians. We also describe the quantum Painlev\'e symmetries at the level of tau functions and, as a byproduct of this analysis, obtain several $\mathbb{C}^2/\mathbb{Z}_2$ blowup relations including those in nontrivial holonomy sectors of the gauge theory.

math-ph↗

arXiv2022

Hamiltonian reductions in Matrix Painlevé systems

For certain finite groups $G$ of Bäcklund transformations we show that the dynamics of $G$-invariant configurations of $n|G|$ Calogero--Painlevé particles is equivalent to certain $n$-particle Calogero--Painlevé system. We also show that the reduction of dynamics on $G$-invariant subset of $n|G|\times n|G|$ matrix Painlevé system is equivalent to certain $n\times n$ matrix Painlevé system. The groups $G$ correspond to folding transformations of Painlevé equations. The proofs are based on the Hamiltonian reductions.

nlin.SI↗