`The O(d,d) Geometry of String Theory'

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.