A class of finite four-dimensional supersymmetric field theories

A class of N=2 supersymmetric models consisting of N=2 Yang-Mills coupled to N=2 matter is shown to be finite to all orders of perturbation theory. For this to hold, the representation of the matter fields must be chosen to give a vanishing one-loop #betta#-function. General N=2 supersymmetric models have a #betta#-function that is determined to all orders in perturbation theory by the one-loop contribution. (orig.)