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

The constraints of N=2 supersymmetry, in combination with several other quire 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 Gamma(U)(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 tau, then this is sufficient to determine the non-perturbative beta-function, given knowledge of its weak coupling behaviour. The result coincides with the outcome of direct calculations from the Seiberg-Witten solution. (C) 1998 Elsevier Science B.V. All rights reserved.