Dynkin Weights and Global Supersymmetry in Grand Unification

Abstract

The requirement that supersymmetry be unbroken in a supersymmetrized gauge theory is shown to imply vanishing Dynkin weight of the components of the Higgs field representation receiving vacuum expectation values. As a corollary a compact expression is obtained for the Dynkin weights of general $\mathrm{SU}\mathrm{}\left(N\right)\mathrm{}$ representations. Examples are given for supersymmetrized grand unified theories.