Double field theory and N=4 gauged supergravity

Double Field Theory describes the NS-NS sector of string theory and lives on a doubled spacetime. The theory has a local gauge symmetry generated by a generalization of the Lie derivative for doubled coordinates. For the action to be invariant under this symmetry, a differential constraint is imposed on the fields and gauge parameters, reducing their possible dependence in the doubled coordinates. We perform a Scherk-Schwarz reduction of Double Field Theory, yielding electric gaugings of half-maximal supergravity in four dimensions when integrability conditions are assumed. The residual symmetries of the compactified theory are mapped with the symmetries of the effective theory and the differential constraints of Double Field Theory are compared with the algebraic conditions on the embedding tensor. It is found that only a weaker form of the differential constraint has to be imposed on background fields to ensure the local gauge symmetry of the reduced action.