The generalised complex geometry of Wess-Zumino-Witten models

In this work a thorough study of a number of specific supersymmetric sigma-models with extended supersymmetry is performed within the context of generalised complex geometry, more specially the supersymmetric Wess-Zumino-Witten model on a variety of group manifolds. By explicitly calculating the admissible complex structures and the associated pure spinors on the target manifold a full characterisation of the different possible geometries is provided. By using this approach the various aspects of generalised Kaehler geometry can be studied in detail. Also considered are the various isometries present in the model and duality relations linking the different descriptions. The examples considered illustrate a weaker definition for a superconformal generalised Kaehler geometry compared to that of a generalised Calabi-Yau geometry. The results suggest that while Wess-Zumino-Witten models provide an excellent example of the various intricacies present in generalised Kaehler geometry, a purely local description is insufficient to fully elucidate phenomena such as type changing which will invariably be present in all but the simplest of examples.