The Spacetime of Double Field Theory: Review, Remarks, and Outlook

TL;DR

This paper reviews double field theory's doubled spacetime, its generalized coordinate transformations, and their role in unifying symmetries, including recent extensions involving ' corrections and non-geometric fluxes.

Contribution

It provides a comprehensive review of DFT's doubled spacetime, generalized transformations, and recent developments like ' extensions and non-geometric backgrounds.

Findings

Generalized coordinate transformations unify diffeomorphisms and gauge transformations.

DFT includes non-geometric flux backgrounds with T-folds.

Recent ' corrections modify the structure of generalized geometry.

Abstract

We review double field theory (DFT) with emphasis on the doubled spacetime and its generalized coordinate transformations, which unify diffeomorphisms and b-field gauge transformations. We illustrate how the composition of generalized coordinate transformations fails to associate. Moreover, in dimensional reduction, the O(d,d) T-duality transformations of fields can be obtained as generalized diffeomorphisms. Restricted to a half-dimensional subspace, DFT includes `generalized geometry', but is more general in that local patches of the doubled space may be glued together with generalized coordinate transformations. Indeed, we show that for certain T-fold backgrounds with non-geometric fluxes, there are generalized coordinate transformations that induce, as gauge symmetries of DFT, the requisite O(d,d;Z) monodromy transformations. Finally we review recent results on the \alpha' extension of DFT which, reduced to the half-dimensional subspace, yields intriguing modifications of the basic structures of generalized geometry.