Supersymmetry and the spontaneous breaking of a U(1) gauge factor

We investigate a supersymmetric theory with an extra U(1) gauge symmetry surviving down to low energies. The extra U(1) is assumed to originate from an E$_6$ grand unified theory (GUT). We show that if one assumes universal soft supersymmetry breaking scalar masses at the GUT scale, and requires the mass of the additional U(1) gauge boson to satisfy phenomenological bounds, then the conditions for electroweak symmetry breaking will provide stringent restrictions on the allowed parameter space of such a theory. We also determine the masses of standard as well as exotic sfermions and find that it is possible for the latter to be lighter than the former. An interesting specific observation is that a light stop is difficult to accommodate with an extra U(1) gauge symmetry.