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

TL;DR

The paper presents a systematic method to classify D- and F-flat directions in N=1 perturbative heterotic string vacua with an anomalous U(1). By leveraging holomorphic gauge-invariant monomials and a basis of one-dimensional flat directions, it shows how the genus-one Fayet-Iliopoulos term can be canceled by vacuum expectation values of non-Abelian singlets while preserving D- and F-flatness and breaking the anomalous U(1). The CHL-5 model is used as a concrete illustration, revealing a structured moduli space of D-flat directions and identifying a subset of flat directions that remain F-flat to all orders. This framework enables systematic exploration of the phenomenological implications of restabilized string vacua and is intended to be applied to broader classes of perturbative string models in future work.

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 canceled 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 address systematically the phenomenological consequences of these models.