From Nonperturbative SUSY Gauge Theories to Integrable Systems

Abstract

I review the appearence of integrable structures in the formulation of exact nonperturbative solutions to $4d$ supersymmetric quantum gauge theories. Various examples of $\mathcal{N}\ge 2$ SUSY Yang-Mills nonperturbative solutions are adequately described in terms of the (deformations of the) finite-gap solutions to integrable models: through the generating differential and the $\tau$-function. One of the basic definitions of generating differential is discussed and its role in the theory of integrable systems is demonstrated.

10 pages, LaTeX, no figures; based on a talk given at 10th International Conference Problems of Quantum Field Theory, 13-18 May 1996, Alushta, Ukraine