Exact information in N=2 theories

Abstract

This is intended to be a simple discussion of work done in collaboration with S. Cecotti, K. Intriligator and C. Vafa; and with H. Saleur. I discuss how $ Tr F (-1)^F e^{-\beta H}$ can be computed exactly in any N=2 supersymmetric theory in two dimensions. It gives exact information on the soliton spectrum of the theory, and corresponds to the partition function of a single self-avoiding polymer looped once around a cylinder of radius $\beta$. It is independent of almost all deformations of the theory, and satisfies an exact differential equation as a function of $\beta$. For integrable theories it can also be computed from the exact S-matrix. This implies a highly non-trivial equivalence of a set of coupled integral equations with the classical sinh-Gordon and the affine Toda equations.