T-folds, doubled geometry, and the SU(2) WZW model

TL;DR

This paper explores the doubled geometry framework applied to the SU(2) WZW model, providing new insights into nongeometric string backgrounds and demonstrating how to recover physical data from doubled descriptions.

Contribution

It presents the T-fold and fully doubled descriptions of WZW models, extending the formalism to general groups and validating it through known physical properties.

Findings

Recovered the physical metric and H-flux from doubled geometry

Reproduced the abelian T-duality group

Matched the semiclassical spectrum of D-branes

Abstract

The SU(2) WZW model at large level N can be interpreted semiclassically as string theory on S^3 with N units of Neveu-Schwarz H-flux. While globally geometric, the model nevertheless exhibits an interesting doubled geometry possessing features in common with nongeometric string theory compactifications, for example, nonzero Q-flux. Therefore, it can serve as a fertile testing ground through which to improve our understanding of more exotic compactifications, in a context in which we have a firm understanding of the background from standard techniques. Three frameworks have been used to systematize the study of nongeometric backgrounds: the T-fold construction, Hitchin's generalized geometry, and fully doubled geometry. All of these double the standard description in some way, in order to geometrize the combined metric and Neveu Schwarz B-field data. We present the T-fold and fully doubled descriptions of WZW models, first for SU(2) and then for general group. Applying the formalism of Hull and Reid-Edwards, we indeed recover the physical metric and H-flux of the WZW model from the doubled description. As additional checks, we reproduce the abelian T-duality group and known semiclassical spectrum of D-branes.