Classification of Flat Directions in Perturbative Heterotic Superstring Vacua with Anomalous U(1)

Abstract 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.