FINITE N = 1 SUSY GAUGE FIELD THEORIES

Abstract

In the present paper we give a detailed description of the method to construct finite N = 1 SUSY gauge field theories in the framework of N = 1 superfields within dimensional regularization. The finiteness of all the Green functions is based on supersymmetry and gauge invariance and is achieved by a proper choice of matter content of the theory and Yukawa couplings in the form yi = fi(ε)g, where g is the gauge coupling, and the function fi(ε) is regular at ε = 0 and is calculated in perturbation theory. Necessary and sufficient conditions for finiteness are determined already in the one-loop approximation. The correspondence with an earlier proposed approach to construct finite theories based on eigenvalue solutions of renormalization-group equations is established.