  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.
