ON THE INTEGRABLE GEOMETRY OF SOLITON-EQUATIONS AND N=2 SUPERSYMMETRIC GAUGE-THEORIES

We provide a unified construction of the symplectic forms which arise in the solution of both N=2 supersymmetric Yang-Mills theories and sol iton 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 symple ctic forms assume explicit expressions in terms of the auxiliary Lax p air, expressions which generalize the well-known Gardner-Faddeev-Zakha rov bracket for KdV to a vast class of 2D integrable models; on the ot her hand, they determine completely the effective Lagrangian and BPS s pectrum 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 less than or equal to N-c + 1 flavors, the spectral curves we obtain this way ag ree with the ones derived by Hanany and Oz and others from physical co nsiderations.