A class of finite four-dimensional supersymmetric field theories

Abstract

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 β-function. General N = 2 supersymmetric models have a β-function that is determined to all orders in perturbation theory by the one-loop contribution.