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Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 198, Number 2, Pages 179–214
DOI: https://doi.org/10.4213/tmf9589 (Mi tmf9589) 		 
This article is cited in 20 scientific papers (total in 20 papers)

Cluster Toda chains and Nekrasov functions

M. A. Bershteinabcde, P. G. Gavrilenkobef, A. V. Marshakovbegh

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
Full-text PDF (1037 kB) Citations (20)
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DOI: https://doi.org/10.4213/tmf9589
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.
Funding agency Grant number
Russian Science Foundation 16-11-10160
Russian Foundation for Basic Research 18-01-00460_а
17-51-50051
Ministry of Education and Science of the Russian Federation 5-100
Contest «Young Russian Mathematics»
The main results obtained in Sec. 2 were supported by a grant from the Russian Science Foundation (Project No. 16-11-10160).
The research of A. V. Marshakov was supported in part by the Russian Foundation for Basic research (Grant No. 17-01-00585) and an RFBR/JSPS joint project (Grant No. 17-51-50051).
This research was also supported by the Russian Academic Excellence Project "5-100."
M. A. Bershtein and P. G. Gavrylenko are Young Russian Mathematics award winners and thank its sponsors and jury.
Received: 26.04.2018
Revised: 26.04.2018
English version:
Theoretical and Mathematical Physics, 2019, Volume 198, Issue 2, Pages 157–188
DOI: https://doi.org/10.1134/S0040577919020016
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. A. Bershtein, P. G. Gavrilenko, A. V. Marshakov, “Cluster Toda chains and Nekrasov functions”, TMF, 198:2 (2019), 179–214; Theoret. and Math. Phys., 198:2 (2019), 157–188
Citation in format AMSBIB
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    • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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