Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 043, 9 pages      hep-th/0703108
Contribution to the Proceedings of the Coimbra Workshop on Geometric Aspects of Integrable Systems

A Journey Between Two Curves

Sergey A. Cherkis a, b
a) School of Mathematics, Trinity College Dublin, Ireland
b) Hamilton Mathematics Institute, TCD, Dublin, Ireland

Received October 31, 2006, in final form February 25, 2007; Published online March 11, 2007

A typical solution of an integrable system is described in terms of a holomorphic curve and a line bundle over it. The curve provides the action variables while the time evolution is a linear flow on the curve's Jacobian. Even though the system of Nahm equations is closely related to the Hitchin system, the curves appearing in these two cases have very different nature. The former can be described in terms of some classical scattering problem while the latter provides a solution to some Seiberg-Witten gauge theory. This note identifies the setup in which one can formulate the question of relating the two curves.

Key words: Hitchin system; Nahm equations; monopoles; Seiberg-Witten theory.

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