On the integrable geometry of soliton equations and N=2 supersymmetric gauge theories
Abstract
We provide a unified construction of the symplectic forms which arise in the solution of both N=2 supersymmetric YangMills theories and soliton equations. Their phase spaces are Jacobiantype bundles over the leaves of a foliation in a universal configuration space. On one hand, imbedded into finitegap solutions of soliton equations, these symplectic forms assume explicit expressions in terms of the auxiliary Lax pair, expressions which generalize the wellknown GardnerFaddeevZakharov bracket for KdV to a vast class of 2D integrable models; on the other hand, they determine completely the effective Lagrangian and BPS spectrum when the leaves are identified with the moduli space of vacua of an N=2 supersymmetric gauge theory. For SU($N_c$) with $N_f\leq N_c+1$ flavors, the spectral curves we obtain this way agree with the ones derived by Hanany and Oz and others from physical considerations.
 Publication:

arXiv eprints
 Pub Date:
 April 1996
 DOI:
 10.48550/arXiv.hepth/9604199
 arXiv:
 arXiv:hepth/9604199
 Bibcode:
 1996hep.th....4199K
 Keywords:

 High Energy Physics  Theory
 EPrint:
 38 pages, TeX file, no figures