An introduction to Seiberg-Witten theory

In their seminal work, Seiberg-Witten showed that the low energy coupling matrix of 4d N=2 supersymmetric theories can be identified with the period matrix of a holomorphic family of Riemann surfaces (most of these words will be defined in the talk). This lead to a series of developments in the understanding of exact non-perturbative results in certain supersymmetric field theories. In this talk, I shall introduce the concept of non-perturbative effects in the form of instantons and show how the proposal by Seiberg-Witten enables us to compute these effects in a pure SU(2) gauge theory.