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 ${\cal N}\geq 2$ 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 $τ$-function. One of the basic definitions of generating differential is discussed and its role in the theory of integrable systems is demonstrated.