Free fermionic webs of heterotic T-folds

TL;DR

This paper explores the diversity of T-folds in string theory with free fermionic descriptions, highlighting how different fermion pairings lead to various moduli configurations and the concept of intrinsically asymmetric T-folds.

Contribution

It introduces the notion of intrinsically asymmetric T-folds and discusses how fermion symmetries extend the T-duality group in non-geometric compactifications.

Findings

Fermionic descriptions can represent multiple T-folds with different moduli.

Some T-folds are intrinsically asymmetric, lacking symmetric orbifold descriptions.

Fermion symmetries extend the T-duality group in these models.

Abstract

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.