The beta-function in N=2 supersymmetric Yang-Mills theory

The constraints of N=2 supersymmetry, in combination with several other quite general assumptions, have recently been used to show that N=2 supersymmetric Yang-Mills theory has a low energy quantum parameter space symmetry characterised by the discrete group ΓU(2). We show that if one also assumes the commutativity of renormalization group flow with the action of this group on the complexified coupling constant τ, then this is sufficient to determine the non-perturbative β-function, given knowledge of its weak coupling behaviour. The result coincides with the outcome of direct calculations from the Seiberg-Witten solution.