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

Abstract

We consider an $O(d,d;\\mathbb{Z})$ invariant massive deformation of double field theory at the level of free theory. We study Kaluza-Klein reduction on ${R}^{1,n\\ensuremath{-}1}\\ifmmode\\times\\else\\texttimes\\fi{}{T}^{d}$ 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 $O(d,d;\\mathbb{Z})$ invariant Fierz-Pauli massive gravity theories.