Free fermionic webs of heterotic T-folds

Moduli stabilisation is key to obtaining phenomenologically viable string models. Non-geometric compactifications, like T-duality orbifolds (T-folds), are capable of freezing many moduli. However, in this Letter we emphasise that T-folds, admitting free fermionic descriptions, can be associated with a large number of different T-folds with varying number of moduli, since the fermion pairings for bosonisation are far from unique. Consequently, in one description a fermionic construction might appear to be asymmetric, and hence non-geometric, while in another it admits a symmetric orbifold description. We introduce the notion of intrinsically asymmetric T-folds for fermionic constructions that do not admit any symmetric orbifold description after bosonisation. Finally, we argue that fermion symmetries induce mappings in the bosonised description that extend the T-duality group.