Toward the M(F )–Theory Embedding of Realistic Free-Fermion Models

We construct a Landau–Ginzburg model with the same data and symmetries as a Z2 × Z2 orbifold that corresponds to a class of realistic free-fermion models. Within the class of interest, we show that this orbifolding connects between different Z2 ×Z2 orbifold models and commutes with the mirror symmetry. Our work suggests that duality symmetries previously discussed in the context of specific M and F theory compactifications may be extended to the special Z2 × Z2 orbifold that characterizes realistic free-fermion models.