Anomalous U(1) and low-energy physics: the power of D-flatness and holomorphy

In models with an anomalous abelian symmetry broken at a very large scale, we study which requirements to impose on the anomalous charges in order to prevent standard model fields from acquiring large vacuum expectation values. The use of holomorphic invariants to study D-flat directions for the anomalous symmetry, proves to be a very powerful tool. We find that in order to forbid unphysical configurations at that scale, the superpotential must contain many interaction terms, including the usual Yukawa terms. Our analysis suggests that the anomalous charge of the μ-term is zero. It is remarkable that, together with the seesaw mechanism, and mass hierarchies, this implies a natural conservation of R-parity.