We describe the dimensional reduction of massive and partially massless spin-2 fields on general Einstein direct product manifolds. As with massless fields, the higher-dimensional gauge symmetry of the partially massless field displays itself upon dimensional reduction as a tower of Stückelberg symmetries for the massive modes of the tower. Unlike the massless case, the zero mode of the gauge symmetry does not display itself as a lower-dimensional non-Stückelberg gauge symmetry enforcing partial masslessness on the zero mode. Partial masslessness is destroyed by the dimensional reduction and the zero-mode gauge symmetry instead serves to eliminate the radion. In addition, we study the fully nonlinear dimensional reduction of de Rham-Gabadadze-Tolley massive gravity on a circle, which results in a massive scalar-tensor-vector theory which we expect to be ghost free, and whose scalar-tensor sector is a special case of mass-varying massive gravity.

• Received 13 December 2016

DOI:https://doi.org/10.1103/PhysRevD.95.024023