Seiberg-Witten Theory, Symplectic Forms, and Hamiltonian Theory of Solitons

Details Seiberg-Witten Theory, Symplectic Forms, and Hamiltonian Theory of Solitons Seiberg-Witten Theory, Symplectic Forms, and Hamiltonian Theory of Solitons

2002-12-26

arxiv.org/abs/hep-th/0212313v1

Physics

High Energy Physics

High Energy Physics - Theory

47 pages, no figures, Beijing and Hangzhou 2002

Scientific paper

This is an expanded version of lectures given in Hangzhou and Beijing, on the symplectic forms common to Seiberg-Witten theory and the theory of solitons. Methods for evaluating the prepotential are discussed. The construction of new integrable models arising from supersymmetric gauge theories are reviewed, including twisted Calogero-Moser systems and spin chain models with twisted monodromy conditions. A practical framework is presented for evaluating the universal symplectic form in terms of Lax pairs. A subtle distinction between a Lie algebra and a Lie group version of this symplectic form is clarified, which is necessary in chain models.

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