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

D'Hoker, Eric; Krichever, I. M.; Phong, D. H.

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

Authors

D'Hoker, Eric

Krichever, I. M.

Phong, D. H.

Description

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.
47 pages, no figures, Beijing and Hangzhou 2002