ONE-LOOP EFFECTS IN N=4 SUPERSYMMETRY

It has been demonstrated that in massless supersymmetric theories, fin ite radiative corrections to the superpotential can occur (viz. the no nrenormalization theorems can he circumvented). In this paper, we exam ine the consequences of this in N = 4 supersymmetric Yang-Mills theory , a model in which the beta function is known to be zero. It is shown that radiative corrections to the superpotential arise at one loop ord er in this theory contrary to the expectations of the nonrenormalizati on theorem, but that their form depends on which formulation of the mo del is used. When one uses a superfield formulation involving an N = 1 vector superfield and three N = 1. chiral superfields in conjunction with a supersymmetric (but not SU(4)) invariant gauge fixing, then at one-loop order, the radiative generation of terms in the superpotentia l means that the equality of the gauge and Yukawa couplings and indeed of different Yukawa couplings is Lost. If one uses the component fiel d formulation of the N = 4 model in the Wess-Zumino gauge with a covar iant, SU(4) invariant (but nor supersymmetric invariant) gauge fixing, then the SU(4) invariance is maintained, but the gauge and Yukawa cou plings are no longer equal. We also consider computations in the compo nent held formulation in the Wess-Zumino gauge using an N = 1 super Ya ng-Mills theory in ten dimensions, dimensionally reduced to four dimen sions, with a ten-dimensional covariant gauge fixing condition. This f ormulation ensures that there is no distinction between gauge and Yuka wa couplings and that SU(4) invariance is automatically preserved; how ever, supersymmetry is broken by the gauge fixing procedure.