We give a geometrical interpretation of the nongeometric $Q$ and $R$ fluxes. To this end, we consider double field theory in a formulation that is related to the conventional one by a field redefinition taking the form of a $T$ duality inversion. The $R$ flux is a tensor under diffeomorphisms and satisfies a nontrivial Bianchi identity. The $Q$ flux can be viewed as part of a connection that covariantizes the winding derivatives with respect to diffeomorphisms. We give a higher-dimensional action with a kinetic term for the $R$ flux and a “dual” Einstein-Hilbert term containing the connection $Q$.

• Received 21 February 2012

DOI:https://doi.org/10.1103/PhysRevLett.108.261602