M. A. Bershtein, P. G. Gavrilenko, A. V. Marshakov, “Cluster Toda chains and Nekrasov functions”, TMF, 2019, Volume 198, Number 2,Pages <nobr>179

This article is cited in 20 papers

Cluster Toda chains and Nekrasov functions

M. A. Bershtein^abcde, P. G. Gavrilenko^bef, A. V. Marshakov^begh

^a Landau Institute for Theoretical Physics, RAS, Moscow Oblast, Chernogolovka, Russia
^b Center for Advanced Studies, Skoltech, Moscow, Russia
^c Independent University of Moscow, Moscow, Russia
^d Information Transmission Problems, RAS, Moscow, Russia
^e Laboratory for Representation Theory and Mathematical Physics, Mathematics Faculty, National Research University Higher School of Economics, Moscow, Russia
^f Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine
^g Institute for Theoretical and Experimental Physics, Moscow, Russia
^h Lebedev Physical Institute, RAS, Moscow, Russia

Abstract: We extend the relation between cluster integrable systems and $q$-difference equations beyond the Painlevé 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.

Keywords: Supersymmetric gauge theories, cluster integrable systems, q-difference Painleve equation.

Received: 26.04.2018
Revised: 26.04.2018

DOI: 10.4213/tmf9589