This article is cited in 31 papers

Modifications of bundles, elliptic integrable systems, and related problems

A. V. Zotov^abc, A. V. Smirnov<sup>ad

a</sup> Institute for Theoretical and Experimental Physics, Moscow, Russia
^b Moscow Institute for Physics and Technology (State University), Dolgoprudnyi, Moscow Oblast, Russia
^c Steklov Mathematical Institute, RAS, Moscow, Russia
^d Department of Mathematics, Columbia University, New York, USA

Abstract: We describe a construction of elliptic integrable systems based on bundles with nontrivial characteristic classes, especially attending to the bundle-modification procedure, which relates models corresponding to different characteristic classes. We discuss applications and related problems such as the Knizhnik–Zamolodchikov–Bernard equations, classical and quantum $R$-matrices, monopoles, spectral duality, Painlevé equations, and the classical–quantum correspondence. For an $SL(N,\mathbb C)$-bundle on an elliptic curve with nontrivial characteristic classes, we obtain equations of isomonodromy deformations.

Keywords: integrable system, Painlevé equation, Hitchin system, modification of bundles.

Received: 20.05.2013

DOI: 10.4213/tmf8551

 English version: Theoretical and Mathematical Physics, 2013, 177:1, 1281–1338

Bibliographic databases:

• 
• 
• 
• 
• 
• 
•