Kaluza-Klein Reduction of Massive and Partially Massless Spin-2 Fields

Abstract

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-Stuckelberg 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 non-linear dimensional reduction of dRGT 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.

32 pages, 1 figure. v2 fixed typos

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• Binary Pulsars as probes for Spin-2 Ultralight Dark Matter
• $\mathcal{N}=2$ Supersymmetric Partially Massless Fields and Non-Unitary Superconformal Representations
• Cosmological model due to dimensional reduction of higher-dimensional massive gravity theory
• Cubic interactions for massless and partially massless spin-1 and spin-2 fields
• Cosmology in warped massive gravity