On "New Massive" 4D Gravity

Eric A. Bergshoeff; Jan Rosseel; J. J. Fernandez-Melgarejo; Paul K. Townsend

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On "New Massive" 4D Gravity

Eric A. Bergshoeff, J. J. Fernandez-Melgarejo, Jan Rosseel, Paul K. Townsend

High Energy Physics - Theory · Submitted 7 Feb 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We construct a four-dimensional (4D) gauge theory that propagates, unitarily, the five polarization modes of a massive spin-2 particle.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.21 · compares with prior results 0.87 · mentions code or data availability 0.02.

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We construct a four-dimensional (4D) gauge theory that propagates, unitarily, the five polarization modes of a massive spin-2 particle. These modes are described by a "dual" graviton gauge potential and the Lagrangian is 4th-order in derivatives. As the construction mimics that of 3D "new massive gravity", we call this 4D model (linearized) "new massive dual gravity". We analyse its massless limit, and discuss similarities to the Eddington-Schroedinger model.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We construct a four-dimensional (4D) gauge theory that propagates, unitarily, the five polarization modes of a massive spin-2 particle.	contribution 1.00	0.95	0.72	asserted 1.00
s1	These modes are described by a "dual" graviton gauge potential and the Lagrangian is 4th-order in derivatives.	method 0.51	0.80	0.13	asserted 1.00
s2	As the construction mimics that of 3D "new massive gravity", we call this 4D model (linearized) "new massive dual gravity".	contribution 0.51	0.66	0.14	asserted 0.99
s3	We analyse its massless limit, and discuss similarities to the Eddington-Schroedinger model.	contribution 0.83	0.87	0.07	asserted 0.74

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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The paper

Original abstract

We construct a four-dimensional (4D) gauge theory that propagates, unitarily, the five polarization modes of a massive spin-2 particle. These modes are described by a "dual" graviton gauge potential and the Lagrangian is 4th-order in derivatives. As the construction mimics that of 3D "new massive gravity", we call this 4D model (linearized) "new massive dual gravity". We analyse its massless limit, and discuss similarities to the Eddington-Schroedinger model.

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References

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Massive Gravity Theories and limits of Ghost-free Bigravity models
hep-th 2012-03 conditional novelty 6.0 of 10

New Massive Gravity and a new class of higher-curvature extensions in any dimension arise as scaling limits of ghost-free Lovelock bigravity, inheriting the absence of the Boulware-Deser ghost.
Bounce and cyclic cosmology in extended nonlinear massive gravity
astro-ph.CO 2012-07 conditional novelty 4.0 of 10

Extended nonlinear massive gravity can accommodate non-singular bounces and cyclic expansion, but the cyclic solutions are reconstructed by imposing a desired oscillatory scale factor and solving for the potential or ...
Galileons in the Sky
astro-ph.CO 2012-04 accept novelty 1.5 of 10

Galileon scalar fields appear in the decoupling limits of several massive-gravity and braneworld models, and their radiative stability makes them viable for inflation and late-time acceleration.

How the literature uses it

17 arXiv papers cite this in 33 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 24 sentences without a confident label

Builds on it 2 papers

Here we generalize the linearized version of the 3D [ref] and 4D [ref] models to arbitrary dimensions by using a rank-3 tensor which satisfies $Ω_μνρ= - Ω_μρν$ and is traceless $η^μνΩ_μνρ=0$.

A note on linearized "New Massive Gravity" in arbitrary dimensions · Introduction · 1.00
Finally, the total action reads S[φ_μ_1⋯μ_d-2,ν]=S_B[φ_μ_1⋯μ_d-2,ν] -m^2 S_E[φ_μ_1⋯μ_d-2,ν] , and it generalizes the NMG actions [ref] to arbitrary dimensions.

Higher-derivative massive actions from dimensional reduction · General $d$ dimensions · 0.95

Uses its method or tool 1 paper

Inspired by [ref] we use the Levi-Civita symbol and define the linear change of variables

A note on linearized "New Massive Gravity" in arbitrary dimensions · Recovering “New Massive” 3D and 4D Gravity · 0.85

Compares with it 1 paper

The result for the parity-odd model is similar to what happens for the 3D TMG model while the result for the parity-even model resembles the parity-even cases in 3D [ref] and 4D [ref] .

On Topologically Massive Spin-2 Gauge Theories beyond Three Dimensions · Discussion · 0.99

Cites it as background 4 papers

In three dimensions, the most interesting theory in this context is the Bergshoeff-Hohm-Townsend (BHT) gravity [ref] , whose generalization to four-dimensional space-time has been proposed in [ref] .

Softly higher-derivative massive gravity · Introduction · 0.88
This realm of research has uncovered many interesting aspects such as its interplay with the physics of diffeomorphism violation [ref] , extra dimensions [ref] , the Stückelberg trick [ref] , linearized [ref] vs. nonlinear massive gravity [ref] , the helicity decomposition of the metric perturbation [ref] , and the Ostrogradsky formalism as well as ghost states [ref] .

Modified-gravity theories with nondynamical background fields · Introduction · 0.99
other three-dimensional theories studied in recent years [ref] .

Super-renormalizable Multidimensional Quantum Gravity · APPENDIX: 3D HIGHER-DERIVATIVE QUANTUM GRAVITY · 0.92

What it cites · 11 sentences without a confident label

Builds on 2 papers

In this paper we have constructed a 4D analog of the linearized 3D massive gravity theory known as “new massive gravity” (NMG) [ref] .

Massive Gravity in Three Dimensions · Conclusions · 0.94
This 3D model was analysed in a different way in [ref] , and here we adapt this analysis to the 4D case.

Massive 3D Supergravity · Massless limit of NMDG · 0.89

Compares with 1 paper

A discontinuity of this sort was to be expected because a similar discontinuity in the number of propagated modes occurs in the massless limit of the 3D NMG, which is what one finds by an application to the Lagrangian ([ref]) of the reduction/truncation procedure of subsection [ref]; i.e. the “pure” fourth-order 3D Lagrangian analysed by Deser [ref] .

Ghost-free, finite, fourth order D=3 (alas) gravity · Massless limit of NMDG · 0.82

Cites as background 2 papers

This possibility has implications for cosmology that have motivated many recent models of “massive gravity”; see [ref] for a recent review.

Theoretical Aspects of Massive Gravity · Introduction · 0.98
Other “exotic” Lorentz representations were explored in [ref] , and the topic has been reconsidered more recently in the context of string/M-theory dualities, see, e.g. [ref] .

Duality in Gravity and Higher Spin Gauge Fields · Introduction · 0.93

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