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

TL;DR

This paper develops methods to classify flat directions in heterotic string vacua with anomalous U(1) gauge groups, crucial for understanding their phenomenology and stability.

Contribution

It introduces systematic techniques for classifying D- and F-flat directions in perturbative heterotic string models with anomalous U(1), including genus-one correction effects.

Findings

Techniques for classifying flat directions are established.

Illustration of methods on a specific heterotic string model.

Framework for analyzing phenomenological implications of string vacua.

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.