RG flow irreversibility, C theorem, and the topological nature of 4D N=2 super-Yang-Mills theory

We determine the exact beta function and a RG flow Lyapunov function for [Formula Presented] super-Yang-Mills (SYM) theory with the gauge group [Formula Presented] It turns out that the classical discriminants of the Seiberg-Witten curves determine the RG potential. The radial irreversibility of the RG flow in the SU(2) case and the nonperturbative identity relating the [Formula Presented] modulus and the superconformal anomaly indicate the existence of a four-dimensional analogue of the [Formula Presented] theorem for [Formula Presented] SYM theory which we formulate for the full [Formula Presented] theory. Our investigation provides further evidence of the essentially topological nature of the theory. © 1998 The American Physical Society.