WHITHAM-TODA HIERARCHY AND N=2 SUPERSYMMETRIC YANG-MILLS THEORY

Abstract

The exact solution of N=2 supersymmetric SU(N) Yang-Mills theory is studied in the framework of the Whitham hierarchies. The solution is identified with a homogeneous solution of a Whitham hierarchy. This integrable hierarchy (Whitham-Toda hierarchy) describes modulation of a quasiperiodic solution of the (generalized) Toda lattice hierarchy associated with the hyperelliptic curves over the quantum moduli space. The relation between the holomorphic pre-potential of the low energy effective action and the τ-function of the (generalized) Toda lattice hierarchy is also clarified.