The dimensional reduction of linearized spin-2 theories invariant under transverse diffeomorphisms

Here we perform the Kaluza–Klein dimensional reduction from D + 1 to D dimensions of massless Lagrangians described by a symmetric rank-2 tensor and invariant under transverse differmorphisms (TDiff). They include the linearized Einstein–Hilbert theory, linearized unimodular gravity and scalar tenso...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 2021-06, Vol.81 (6), p.1-14, Article 547
Main Authors: Dalmazi, D., dos Santos, R. R. Lino
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Cosmology
Couplings
Elementary Particles
Ghosts
Gravitational waves
Gravity
Hadrons
Heavy Ions
Invariants
Isomorphism
Linearization
Mathematical analysis
Measurement Science and Instrumentation
Nuclear Energy
Nuclear Physics
Parameterization
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Reduction
Regular Article - Theoretical Physics
String Theory
Symmetry
Tensors
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Summary:Here we perform the Kaluza–Klein dimensional reduction from D + 1 to D dimensions of massless Lagrangians described by a symmetric rank-2 tensor and invariant under transverse differmorphisms (TDiff). They include the linearized Einstein–Hilbert theory, linearized unimodular gravity and scalar tensor models. We obtain simple expressions in terms of gauge invariant field combinations and show that unitarity is preserved in all cases. After fixing a gauge, the reduced model becomes a massive scalar tensor theory. We show that the diffeomorphism (Diff) symmetry, instead of TDiff, is a general feature of the massless sector of consistent massive scalar tensor models. We discuss some subtleties when eliminating Stückelberg fields directly at action level as gauge conditions. A non local connection between the massless sector of the scalar tensor theory and the pure tensor TDiff model leads to a parametrization of the non conserved source which naturally separates spin-0 and spin-2 contributions in the pure tensor theory. The case of curved backgrounds is also investigated. If we truncate the non minimal couplings to linear terms in the curvature, vector and scalar constraints require Einstein spaces as in the Diff and WTDiff (Weyl plus Diff) cases. We prove that our linearized massive scalar tensor models admit those curved background extensions.
ISSN:1434-6044
1434-6052
DOI:10.1140/epjc/s10052-021-09297-0