On the integrable geometry of soliton equations and N=2 supersymmetric gauge theories

Details On the integrable geometry of soliton equations and N=2 supersymmetric gauge theories On the integrable geometry of soliton equations and N=2 supersymmetric gauge theories

1996-04-30

arxiv.org/abs/hep-th/9604199v1

J.Diff.Geom. 45 (1997) 349-389

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, TeX file, no figures

Scientific paper

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($N_c$) 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.

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