In flat space, massless fields with spin always come with a gauge invariance, which their massive counterparts lack. When performing Kaluza Klein (KK) reduction to fewer dimensions, these gauge symmetries become lower dimensional, and are either associated with algebraic Stuckelberg-like fields (when these are gauge fixed, the KK modes eat and acquire their masses), or are zero modes (which generate true gauge transformations on the massless KK modes). In curved spacetime, there is an additional case: a partially massless (PM) field, which comes with a reduced gauge symmetry. In the case of PM gravity, the zero mode of this symmetry does not gauge transform the massless KK mode, but instead removes it. Here, the KK reduction of PM and massive gravity is performed, giving massive scalar-vector-tensor theories in lower dimensions.

This is significant for a number of reasons. Firstly, after projecting out the massive KK vector mode, one is left with a lower dimensional massive scalar-tensor theory which can be recognized as a particular massive gravity model with varying mass. The fact that this theory can be obtained from the reduction of a healthy theory suggests that they are also healthy. Second, the massless KK mode (the radion) is often the source of instabilities, and now we see that the PM symmetry successfully removes it.