Vanishing Renormalization of theDTerm in Supersymmetric U(1) Theories

Abstract

The breaking of supersymmetry can be implemented by the $D$ term. This term can be quadratically divergent, ruining the possibility of naturally large hierarchies. According to Witten this does not occur if the U(1) gauge group is unified in a semisimple group. We show that sufficient conditions for the $D$ counterterm to vanish are less restrictive than grand unification and only require a vanishing trace of the U(1) charge. No cancellation between high-energy and low-energy scales is involved.