Abstract

I will briefly review the T-duality of string theory and how double field theory gives a manifestly T-duality invariant action for 10-d SUGRA at the cost of introducing new coordinates related to the winding modes of strings. Double field theory not only combines the NS-NS sector of 10-d SUGRA into a generalised metric but also combines the infinitesimal symmetries into a generalised Lie derivative. In order to define a covariant derivative with respect to this Lie derivative requires a new geometry which can be built using a flat but torsionful connection. The geometric information is now fully contained in the torsion and I will show how to use this torsion to construct the double field theory action. If time permits I will discuss how this relates to the action of gauged supergravities using the Scherk-Schwarz procedure.