TDiff and Weyl Invariant Massive Spin-2: Linear Theory

TL;DR

This paper constructs novel flat-space massive spin-2 Lagrangians with Weyl and transverse-diffeomorphism symmetries via Kaluza-Klein reduction, providing an alternative to Fierz-Pauli theory that is physically equivalent and generalizable.

Contribution

It introduces a new class of massive spin-2 Lagrangians with enhanced gauge symmetries derived from higher-dimensional theories, expanding the theoretical framework beyond Fierz-Pauli.

Findings

Lagrangians differ from Fierz-Pauli but are physically equivalent

Auxiliary fields naturally emerge from higher-dimensional construction

Generalization to spin-2 fields on Einstein manifolds achieved

Abstract

We use Kaluza-Klein reduction to construct flat-space massive spin-2 Lagrangians based on a kinetic term that has local Weyl and transverse-diffeomorphism gauge symmetries in the massless limit. This yields Lagrangians describing a free massive spin 2 which differ from the usual Fierz-Pauli theory, but are physically equivalent to it. These Lagrangians require the use of auxiliary fields, which appear naturally from the higher-dimensional construction. We discuss how these Lagrangians are related to each other and to the Fierz-Pauli theory through St\"uckelberg transformations, gauge fixings, and field replacements, and we use this to generalize the construction to spin-2 fields on Einstein manifolds.