Flat directions in three-generation free-fermionic string models

In quasi-realistic string models that contain an anomalous U(1) the non-zero Fayet-Iliopoulos term triggers the shifting of the original vacuum to a new one along some flat direction, so that SUSY is preserved but the gauge group is partially broken. The phenomenological study of these models thus requires as a first step the mapping of the space of flat directions. We investigate F- and D-flat directions in several three-generation SU(3) sub C x SU(2) sub L x U(1) sub Y free-fermionic string models and discuss the typical scenarios that generically arise. When they exist, we systematically construct the flat directions that preserve hypercharge, only break abelian group factors, and can be proven to remain F-flat to all orders in the non-renormalizable superpotential.