Cubic action in double field theory

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