TDiff and Weyl Invariant Massive Spin-2: Linear Theory

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 Stückelberg transformations, gauge fixings, and field replacements, and we use this to generalize the construction to spin-2 fields on Einstein manifolds.

37 pages, 2 figures. v3 some statements on equivalence corrected

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• The path integral of unimodular gravity
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• Resonances at the LHC beyond the Higgs: The Scalar/Tensor Case
• The decoupling limit of Multi-Gravity: Multi-Galileons, Dualities and More
• Weyl relativity: A novel approach to Weyl's ideas
• Structures in multiple spin-2 interactions
• The dimensional reduction of linearized spin-2 theories invariant under transverse diffeomorphisms
• Impossible Symmetries and Conformal Gravity
• Note on massless and partially massless spin-2 particles in a curved background via a nonsymmetric tensor
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• Weyl and transverse diffeomorphism invariant spin-2 models in D=2+1
• Massive Unimodular Gravity
• Nonexistence of a parent theory for general relativity and unimodular gravity
• Duality as a Method to Derive a Gauge Invariant Massive Electrodynamics and New Interactions
• Absence of the Higuchi bound in a family of alternative linear massive spin-2 models