On “new massive” 4D gravity

Bergshoeff, Eric; Fernandez-Melgarejo, Jose J.; Rosseel, Jan; Townsend, Paul

doi:10.1007/jhep04(2012)070

Cited by 27 publications

(70 citation statements)

References 31 publications

(53 reference statements)

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“…We explain why the equations of motion of (49) can be written as a set of zero "curvature" conditions. In section V we recover the linearized NMG in D = 3 [13] and in D = 4 [16]. In section VI we draw our conclusions and perspectives.…”

Section: Introductionmentioning

confidence: 90%

“…Although the minimal tensor structure to describe massive spin-2 particles is a symmetric rank-2 tensor, in order to derive a higher derivative unitary model it is convenient, see [16], to start with the first-order description of the Einstein-Hilbert theory (massless action) in terms of the vielbein and spin-connection. After linearization around a flat background and addition of the Fierz-Pauli mass term we have:…”

Section: Higher Derivative Spin-1 Modelmentioning

confidence: 99%

“…A step toward a generalization of [13] to D > 3 has been taken in [16] where a linearized version of a possible NMG in D = 4 is suggested. The model has been shown to be unitary.…”

Section: Introductionmentioning

confidence: 99%

“…The model has been shown to be unitary. While the 3D NMG model is usually formulated in terms of a symmetric rank-2 tensor, the 4D model of [16] is given in terms of a rank-3 tensor satisfying T Here we generalize the linearized version of the 3D [13] and 4D [16] models to arbitrary dimensions by using a rank-3 tensor which satisfies Ω µνρ = −Ω µρν and is traceless η µν Ω µνρ = 0.…”

Section: Introductionmentioning

confidence: 99%

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Note on linearized “new massive gravity” in arbitrary dimensions

Dalmazi

Santos

2013

Phys. Rev. D

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By means of a triple master action we deduce here a linearized version of the "New Massive Gravity" (NMG) in arbitrary dimensions. The theory contains a 4th-order and a 2nd-order term in derivatives. The 4th-order term is invariant under a generalized Weyl symmetry. The action is formulated in terms of a traceless η µν Ω µνρ = 0 mixed symmetry tensor Ω µνρ = −Ω µρν and corresponds to the massive Fierz-Pauli action with the replacement e µν = ∂ ρ Ω µνρ . The linearized 3D and 4D NMG theories are recovered via the invertible maps Ω µνρ = ǫ

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Section: Introductionmentioning

confidence: 90%

Section: Higher Derivative Spin-1 Modelmentioning

confidence: 99%

“…A step toward a generalization of [13] to D > 3 has been taken in [16] where a linearized version of a possible NMG in D = 4 is suggested. The model has been shown to be unitary.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Note on linearized “new massive gravity” in arbitrary dimensions

Dalmazi

Santos

2013

Phys. Rev. D

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“…In Ref. [23] one finds further evidence in favor of d À ¼ 1, since the linearized new massive gravity in three [24] and four dimensions [23] can be directly (at action level) deduced from L FP ðd À ¼ 1Þ by a derivative field redefinition which holds even at coinciding points (no contact terms). For instance, one can choose (see Ref.…”

Section: Discussionmentioning

confidence: 93%

Note on the nonuniqueness of the massive Fierz-Pauli theory and spectator fields

Dalmazi

2013

Phys. Rev. D

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It is possible to show that there are three independent families of models describing a massive spin-2 particle via a rank-2 tensor. One of them contains the massive Fierz-Pauli model, the only case described by a symmetric tensor. The three families have different local symmetries in the massless limit and can not be interconnected by any local field redefinition. We show here, however, that they can be related with the help of a decoupled and nondynamic (spectator) field. The spectator field may be either an antisymmetric tensor B ¼ ÀB , a vector A or a scalar field ', corresponding to each of the three families. The addition of the extra field allows us to formulate master actions which interpolate between the symmetric Fierz-Pauli theory and the other models. We argue that massive gravity models based on the Fierz-Pauli theory are not expected to be equivalent to possible local self-interacting theories built up on top of the two new families of massive spin-2 models. The approach used here may be useful to investigate dual (nonsymmetric) formulations of higher-spin particles.

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The holographic c-theorem and infinite-dimensional Lie algebras

Bergshoeff

Ozkan

Zog

2022

J. High Energ. Phys.

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We discuss a non-dynamical theory of gravity in three dimensions which is based on an infinite-dimensional Lie algebra that is closely related to an infinite-dimensional extended AdS algebra. We find an intriguing connection between on the one hand higher-derivative gravity theories that are consistent with the holographic c-theorem and on the other hand truncations of this infinite-dimensional Lie algebra that violate the Lie algebra structure. We show that in three dimensions different truncations reproduce, up to terms that do not contribute to the c-theorem, Chern-Simons-like gravity models describing extended 3D massive gravity theories. Performing the same procedure with similar truncations in dimensions larger than or equal to four reproduces higher derivative gravity models that are known in the literature to be consistent with the c-theorem but do not have an obvious connection to massive gravity like in three dimensions.

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On “new massive” 4D gravity

Cited by 27 publications

References 31 publications

Note on linearized “new massive gravity” in arbitrary dimensions

Note on linearized “new massive gravity” in arbitrary dimensions

Note on the nonuniqueness of the massive Fierz-Pauli theory and spectator fields

The holographic c-theorem and infinite-dimensional Lie algebras

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