Conformal chiral boson models on twisted doubled tori and non-geometric string vacua

Abstract

We derive and analyze the conditions for quantum conformal and Lorentz invariance of the duality symmetric interacting chiral boson sigma-models, which are conjectured to describe non-geometric string theory backgrounds. The one-loop Weyl and Lorentz anomalies are computed for the general case using the background field method. Subsequently, our results are applied to a class of (on-shell) Lorentz invariant chiral boson models which are based on twisted doubled tori. Our findings are in agreement with those expected from the effective supergravity approach, thereby firmly establishing that the chiral boson models under consideration provide the string worldsheet description of N = 4 gauged supergravities with electric gaugings. Furthermore, they demonstrate that twisted doubled tori are indeed the doubled internal geometries underlying a large class of non-geometric string compactifications. For compact gaugings the associated chiral boson models are automatically conformal, a fact that is explained by showing that they are actually chiral WZW models in disguise.