$T$-folds from Yang-Baxter deformations

TL;DR

This paper explores the non-geometric nature of Yang-Baxter deformed backgrounds in string theory, revealing their structure as T-folds with non-trivial monodromies and fluxes, extending understanding beyond local geometries.

Contribution

It demonstrates that Yang-Baxter deformations can be viewed as T-folds with explicit O(D,D;Z) monodromies and extends the non-geometric perspective to solutions of generalized supergravity equations beyond YB deformations.

Findings

YB-deformed backgrounds are T-folds with O(D,D;Z) monodromy.

Non-Abelian T-duality solutions can also be T-folds.

Solutions of GSE are generally non-geometric.

Abstract

Yang-Baxter (YB) deformations of type IIB string theory have been well studied from the viewpoint of classical integrability. Most of the works, however, are focused upon the local structure of the deformed geometries and the global structure still remains unclear. In this work, we reveal a non-geometric aspect of YB-deformed backgrounds as $T$-fold by explicitly showing the associated $\mathrm{O}(D,D;\mathbb{Z})$ $T$-duality monodromy. In particular, the appearance of an extra vector field in the generalized supergravity equations (GSE) leads to the non-geometric $Q$-flux. In addition, we study a particular solution of GSE that is obtained by a non-Abelian $T$-duality but cannot be expressed as a homogeneous YB deformation, and show that it can also be regarded as a $T$-fold. This result indicates that solutions of GSE should be non-geometric quite in general beyond the YB deformation.