Duality in Integrable Systems and Gauge Theories

Abstract

We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as allow to construct new ones, double elliptic among them. We also discuss applications to the (supersymmetric) gauge theories in various dimensions.

harvmac 45 pp.; v4. minor corrections, to appear in JHEP

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