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

TL;DR

This paper investigates how massive and partially massless spin-2 fields behave under dimensional reduction on Einstein manifolds, revealing differences from massless cases and exploring implications for massive gravity theories.

Contribution

It provides a detailed analysis of the Kaluza-Klein reduction of spin-2 fields, highlighting the fate of gauge symmetries and partial masslessness, and studies the non-linear reduction of dRGT massive gravity.

Findings

Partial masslessness is broken by dimensional reduction.

Zero mode gauge symmetry eliminates the radion.

Derived a ghost-free scalar-tensor-vector theory from massive gravity.

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 St\"uckelberg 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.