Properties of double field theory

In this thesis we study several aspects of Double Field Theory (DFT). In
general, Double Field Theory is subject to the so-called strong constraint. By
using the Flux Formulation of DFT, we explore to what extent one can deal
with the gauge consistency constraints of DFT without imposing the strong
constraint. We introduce the generalized fluxes, which are higher-dimensionalelds that upon compactication give rise to the usual constant
fluxes (i.e., the gaugings of gauged supergravities). We rely on a geometric construction in order to build geometric quantities like the generalized Ricci scalar. The novel notions of stringy differential geometry are adapted to hold beyond the strong constraint. We move on to study the usual chain of brane solutions known as NS5-KK5-Q5 (or 522) and R5 in the DFT language. We argue that the R5-brane solution has a winding coordinate-dependence rendering it locally non-geometric from the usual supergravity point of view. We justify this by using a generalized Scherk-Schwarz reduction ansatz of DFT. Finally, we construct the dual theory of Double Field Theory, which we call Dual Double Field Theory. This theory incorporates all the mixed-symmetry potentials that couple naturally to the
branes mentioned before. We consider a dualization procedure proposing a
first-order action in the Flux Formulation and also in a geometric formulation
using the spin connection. The Dual DFT reduces to the standard dualization
for the NS-elds in standard space.