1996/04/30 by I. M. Krichever, D. H. Phong
Physics and Astronomy · #hep-th
published as J.Diff.Geom. 45 (1997) 349-389 · 38 pages, TeX file, no figures
arxiv created 1996/04/30 · arxiv updated 2009/11/30
We provide a unified construction of the symplectic forms which arise in the solution of both N=2 supersymmetric Yang-Mills theories and soliton equations. Their phase spaces are Jacobian-type bundles over the leaves of a foliation in a universal configuration space. On one hand, imbedded into finite-gap solutions of soliton equations, these symplectic forms assume explicit expressions in terms of the auxiliary Lax pair, expressions which generalize the well-known Gardner-Faddeev-Zakharov 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(Nc) with Nf≤ Nc+1 flavors, the spectral curves we obtain this way agree with the ones derived by Hanany and Oz and others from physical considerations.