Nongeometry, Duality Twists, and the Worldsheet

In this paper, we use orbifold methods to construct nongeometric backgrounds, and argue that they correspond to the spacetimes discussed in \cite{dh,wwf}. More precisely, we make explicit through several examples the connection between interpolating orbifolds and spacetime duality twists. We argue that generic nongeometric backgrounds arising from duality twists will not have simple orbifold constructions and then proceed to construct several examples which do have a consistent worldsheet description.