SeibergWitten Theory, Symplectic Forms, and Hamiltonian Theory of Solitons
Abstract
This is an expanded version of lectures given in Hangzhou and Beijing, on the symplectic forms common to SeibergWitten 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 CalogeroMoser 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2002
 DOI:
 10.48550/arXiv.hepth/0212313
 arXiv:
 arXiv:hepth/0212313
 Bibcode:
 2002hep.th...12313D
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Complex Variables
 EPrint:
 47 pages, no figures, Beijing and Hangzhou 2002