From free-fermionic constructions to orbifolds and back

We systematically develop the explicit map between string vacua constructed in the Free Fermionic Formulation and their ${\mathbb{Z}}_2^N$ \( {\mathbb{Z}}_2^N \) toroidal orbifold counterparts. We illustrate the map in various example classes of models, including cases relevant for string phenomenology, as well as in theories where space-time supersymmetry is broken by the stringy Scherk-Schwarz mechanism.