Academic Year 2007/2008

T-duality originally arises as a symmetry of string theory which relates string theory compactified on large circles with string theory compactified on small circles. Locally the transformation rules of the low energy effective fields under T-duality are given by the well-known Buscher rules, however global issues in the presence of NS 3-form H-flux have remained obscure. Through examples in the literature, it is argued that T-duality lead to a topology change of the underlying manifold . Many open questions regarding T-duality in the presence of background fluxes remain to be answered though. In order to understand the topology change under T-duality, a systematic method has been developed by Bouwknegt, Evslin and Mathai. It was recently discovered by Gualtieri and Cavalcanti that Generalized geometry provides a natural setting to study T-duality. In this talk we will review basic settings of Generalized geometry, concepts of topological T-duality constructed by Bouwknegt, Evslin and Mathai, and how to extend T-duality in the context of Generalized geometry. In particular, we extend the results by Gualtieri and Cavalcanti of principal circle bundles to general principal torus bundles with a generalization of the Courant bracket which is invariant under T-duality transformation in the presence of non-trivial background flux. At the end we show how Lie algebroid theory can be applied to interpret our result.