D-Moduli Stabilization

The matter sector of four-dimensional effective supergravity models obtained from the weakly coupled heterotic string contains many moduli. In particular, flat directions of the D-term part of the scalar potential in the presence of an anomalous U(1) give rise to massless chiral multiplets which have been referred to elsewhere as Dmoduli. The stabilization of these moduli is necessary for the determination of the large vacuum expectation values of complex scalar fields induced by the corresponding Fayet-Illiopoulos term. This stabilization is of phenomenological importance since these background values determine the effective theory below the scale of the anomalous U(1) symmetry breaking. In some simple models we illustrate the stabilization of these moduli due to the nonperturbative dynamics associated with gaugino condensation in a hidden sector. We find that background field configurations which are stable above the condensation scale no longer represent global minima once dynamical supersymmetry breaking occurs. The implications for low energy models based on promising “flat” directions are discussed.