Generalised T-Duality and Non-Geometric Backgrounds

TL;DR

This work identifies and systematizes non-geometric string backgrounds by lifting a broad class of gauged supergravities to ten dimensions, revealing a new class with nontrivial dependence on dual coordinates conjugate to winding. It shows that generalized T-duality can act beyond isometries and that such backgrounds arise naturally in string field theory and the doubled geometry framework, including T-folds and their asymmetries. At special moduli, some constructions reduce to asymmetric orbifolds, linking the new backgrounds to well-understood consistent string backgrounds. A universal bosonic sector and scalar potential underpin the gauged supergravities, with concrete realization in WZW-model deformations, illustrating non-linear structure and symmetry-breaking patterns. Overall, the paper extends the landscape of consistent string backgrounds and provides a framework for exploring further non-geometric phases via duality, doubled geometry, and string field theory.

Abstract

We undertake a systematic analysis of non-geometric backgrounds in string theory by seeking stringy liftings of a class of gauged supergravity theories. In addition to conventional flux compactifications and non-geometric T-folds with T-duality transition functions, we find a new class of non-geometric backgrounds with non-trivial dependence on the dual coordinates that are conjugate to the string winding number. We argue that T-duality acts in our class of theories, including those cases without isometries in which the conventional Buscher rules cannot be applied, and that these generalised T-dualities can take T-folds or flux compactifications on twisted tori to examples of the new non-geometric backgrounds. We show that the new class of non-geometric backgrounds and the generalised T-dualities arise naturally in string field theory, and are readily formulated in terms of a doubled geometry, related to generalised geometry. At special points in moduli space, some of the non-geometric constructions become equivalent to asymmetric orbifolds which are known to provide consistent string backgrounds. We construct the bosonic sector of the corresponding gauged supergravity theories and show that they have a universal form in any dimension, and in particular construct the scalar potential. We apply this to the supersymmetric WZW model, giving the complete non-linear structure for a class of WZW-model deformations.