Classification of flat directions in perturbative heterotic superstring vacua with anomalous U(1)

We develop techniques to classify D- and F-flat directions for N = 1 supersymmetric string vacua of the perturbative heterotic string theory, which possess an anomalous U(1) gauge group at the tree level. Genus-one corrections generate a Fayet-Iliopoulos term for the D-term of U(1)_A, which is cancelled by non-zero vacuum expectation values (VEVs) of certain massless multiplets, in such a way that the anomalous U(1) is broken, while maintaining the D- and F-flatness of the effective field theory. A systematic analysis of flat directions is given for non-zero VEVs of non-Abelian singlets, and the techniques are illustrated for a specific model. The approach sets the stage to classify the D- and F-flat directions for a large class of perturbative string vacua. This classification is a prerequisite to systematically addressing the phenomenological consequences of these models.