CLUSTER TODA CHAINS AND NEKRASOV FUNCTIONS

被引：20

作者：

Bershtein, M. A. ^{[1
,2
,3
,4
,5
]}

Gavrylenko, P. G. ^{[1
,2
,6
]}

Marshakov, A. V. ^{[1
,2
,7
,8
]}

机构：

[1] RAS, Landau Inst Theoret Phys, Chernogolovka, Moscow Oblast, Russia

[2] Natl Res Univ Higher Sch Econ, Lab Representat Theory & Math Phys, Fac Math, Moscow, Russia

[3] Skoltech, Ctr Adv Studies, Moscow, Russia

[4] Independent Univ Moscow, Moscow, Russia

[5] RAS, Inst Informat Transmiss Problems, Moscow, Russia

[6] Bogolyubov Inst Theoret Phys, Kiev, Ukraine

[7] Inst Theoret & Expt Phys, Moscow, Russia

[8] RAS, Theory Dept, Lebedev Phys Inst, Moscow, Russia

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2019年 / 198卷 / 02期

基金：

俄罗斯科学基金会; 俄罗斯基础研究基金会;

关键词：

integrable system; topological string; cluster algebra; supersymmetric gauge theory;

D O I：

10.1134/S0040577919020016

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We extend the relation between cluster integrable systems and q-difference equations beyond the Painlev ' e case. We consider the class of hyperelliptic curves where the Newton polygons contain only four boundary points. We present the corresponding cluster integrable Toda systems and identify their discrete automorphisms with certain reductions of the Hirota difference equation. We also construct nonautonomous versions of these equations and find that their solutions are expressed in terms of five-dimensional Nekrasov functions with Chern-Simons contributions, while these equations in the autonomous case are solved in terms of Riemann theta functions.

引用

页码：157 / 188

页数：32

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