O (d ,d ;Z ) invariant Fierz-Pauli massive gravity

We consider an O (d ,d ;Z ) invariant massive deformation of double field theory at the level of free theory. We study Kaluza-Klein reduction on R^{1 ,n -1}×T^d and derive the diagonalized second order action for each helicity mode. Imposing the absence of ghosts and tachyons, we obtain a class of consistency conditions which include the well-known weak constraint in double field theory as a special case. Consequently, we find two-parameter sets of O (d ,d ;Z ) invariant Fierz-Pauli massive gravity theories.