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.