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Dualities in integrable systems: geometrical aspects

A. Gorsky·V. Rubtsov
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Abstract

We discuss geometrical aspects of different dualities in the integrable systems of the Hitchin type and its various generalizations. It is shown that T duality known in the string theory context is related to the separation of variables procedure in dynamical system. We argue that there are analogues of S duality as well as mirror symmetry in the many-body systems of Hitchin type. The different approaches to the double elliptic systems are unified using the geometry behind the Mukai-Odesskii algebra.

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A. Gorsky, V. Rubtsov. 2001-03-01. Dualities in integrable systems: geometrical aspects. https://arxiv.org/abs/hep-th/0103004

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