  We study target space theory on a torus for the states with $N_L+N_R=2$
through Double Field Theory. The spin-two Fierz-Pauli fields are not allowed
when all spatial dimensions are non-compact. The massive states provide both
non-vanishing momentum and winding numbers in the target space theory. To
derive the cubic action, we provide the unique constraint for $N_L\neq N_R$
compatible with the integration by part. We first make a correspondence of
massive and massless fields. The quadratic action is gauge invariant by
introducing the mass term. We then proceed to the cubic order. The cubic action
is also gauge invariant by introducing the coupling between the one-form field
and other fields. The massive states do not follow the consistent truncation.
One should expect the self-consistent theory by summing over infinite modes.
Hence the naive expectation is wrong up to the cubic order. In the end, we show
that the momentum and winding modes cannot both appear for only one compact
doubled space.
