Cluster Toda Chains and Nekrasov Functions
Abstract
We extend the relation between cluster integrable systems and qdifference equations beyond the Painleev 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 fivedimensional Nekrasov functions with ChernSimons contributions, while these equations in the autonomous case are solved in terms of Riemann theta functions.
 Publication:

Theoretical and Mathematical Physics
 Pub Date:
 February 2019
 DOI:
 10.1134/S0040577919020016
 arXiv:
 arXiv:1804.10145
 Bibcode:
 2019TMP...198..157B
 Keywords:

 integrable system;
 topological string;
 cluster algebra;
 supersymmetric gauge theory;
 Mathematical Physics;
 High Energy Physics  Theory;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 32 pages, 13 figures, small corrections, references added