Modular invariant gaugino condensation in the presence of an anomalous U(1)

Starting from the previously constructed effective supergravity theory below the scale of U(1) breaking in orbifold compactifications of the weakly coupled heterotic string, we study the effective theory below the scale of supersymmetry breaking by gaugino and matter condensation in a hidden sector. Questions we address include vacuum stability and the masses of the various moduli fields, including those associated with flat directions at the U(1) breaking scale, and of their fermionic superpartners. The issue of soft supersymmetry-breaking masses in the observable sector presents a particularly serious challenge for this class of models.