Duality for symmetric second rank tensors: The massive case

Casini, Horacio; Montemayor, R.; Urrutia, L. F.

doi:10.1103/physrevd.66.085018

Cited by 21 publications

(55 citation statements)

References 38 publications

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“…It has the form of a Lagrangian in our multiparametric family, but with h µν without a definite symmetry, instead of the symmetric one chosen in [16,17]. When T α [µν] is eliminated from this first order Lagrangian, the antisymmetric part of h µν decouples and becomes irrelevant, so that we obtain the usual massive Fierz-Pauli theory.…”

Section: Jhep09(2008)058mentioning

confidence: 99%

“…This is exhibited as a simple example of the ambiguities in the dual theory introduced by constructing the parent Lagrangian with arbitrary coefficients, restricted only by the condition that after eliminating the field ω α[βγ] the standard FP theory is recovered, as it is done in refs. [16,17]. Nevertheless, given that we arrive at the condition a = 0 only after a very particular gauge fixing and field elimination via equations of motion, we take this as an indication that these two generally non-commuting and non-unique processes will also introduce ambiguities in the final Zinoviev Lagrangian containing only the dual propagating field.…”

Section: The Curtright-freund Action From the Zinoviev Parent Actionmentioning

confidence: 99%

“…[19] a duality transformation between Stueckelberg-like Lagrangians for massive fields is obtained, while in that of refs. [16,17] the duality is directly stated at the level of the fields h αβ and T ρ [µν] corresponding to different representations for the massive spin two degrees of freedom. When comparing with works of Zinoviev one has to keep in mind that his metric is diag(+, −, −, −) so that we will need to make the appropriate changes of signs to translate his results into those corresponding to our choice of the metric.…”

Section: The Zinoviev Approach and The Curtright-freund Formulation Imentioning

confidence: 99%

“…[16,17], which dispensed from the gauge invariance requirements of the action dual to FP. The starting point of the procedure is a second order Lagrangian in four dimensions, which depends on the fields ϕ a and their derivatives ∂ µ ϕ a .…”

Section: Jhep09(2008)058mentioning

confidence: 99%

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Duality for massive spin two theories in arbitrary dimensions

González

Khoudeir

Montemayor

et al. 2008

J. High Energy Phys.

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Using the parent Lagrangian approach we construct a dual formulation, in the sense originally proposed by Curtright and Freund, of a massive spin two Fierz-Pauli theory in arbitrary dimensions D. This is achieved in terms of a mixed symmetry tensor, without the need of auxiliary fields. The relation of this method with an alternative formulation based on a gauge symmetry principle proposed by Zinoviev is elucidated. We show that the latter formulation in four dimensions, with a given gauge fixing together with a definite sequence of auxiliary fields elimination via their equations of motion, leads to the parent Lagrangian already considered by West completed by a FierzPauli mass term, which in turns yields the Curtright-Freund action. This motivates our generalization to arbitrary dimensions leading to the corresponding extension of the four dimensional result. We identify the transverse true degrees of freedom of the dual theory and verify that their number is in accordance with those of the massive Fierz-Pauli field.

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Section: Jhep09(2008)058mentioning

confidence: 99%

Section: The Curtright-freund Action From the Zinoviev Parent Actionmentioning

confidence: 99%

Section: The Zinoviev Approach and The Curtright-freund Formulation Imentioning

confidence: 99%

Section: Jhep09(2008)058mentioning

confidence: 99%

See 2 more Smart Citations

Duality for massive spin two theories in arbitrary dimensions

González

Khoudeir

Montemayor

et al. 2008

J. High Energy Phys.

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“…Analogous to L FP ðd À Þ, the massless limit of L nFP ðcÞ describes a massless spin-2 particle (see Refs. [15,19]), which is invariant under linearized reparametrizations plus Weyl transformations,…”

Section: Three Familiesmentioning

confidence: 99%

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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On the degrees of freedom of R2 gravity in flat spacetime

Hell,

Lüst,

Zoupanos

2024

J. High Energ. Phys.

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We study the degrees of freedom of R2 gravity in flat spacetime with two approaches. By rewriting the theory a la Stueckelberg, and implementing Lorentz-like gauges to the metric perturbations, we confirm that the pure theory propagates one scalar degree of freedom, while the full theory contains two tensor modes in addition. We then consider the degrees of freedom by directly examining the metric perturbations. We show that the degrees of freedom of the full theory match with those obtained with the manifestly covariant approach. In contrast, we find that the pure R2 gravity has no degrees of freedom. We show that a similar discrepancy between the two approaches appears also in a theory dual to the three-form, and appears due to the Lorentz-like gauges, which lead to the fictitious modes even after the residual gauge redundancy has been taken into account. At first sight, this implies a discontinuity between the full theory and the pure case. By studying the first-order corrections of the full R2 gravity beyond the linear regime, we show that at high-energies, both scalar and tensor degrees of freedom become strongly coupled. This implies that the apparent discontinuity of pure and full R2 gravity is just an artefact of the perturbation theory, and further supports the absence of degrees of freedom in the pure R2 gravity.

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Duality for symmetric second rank tensors: The massive case

Cited by 21 publications

References 38 publications

Duality for massive spin two theories in arbitrary dimensions

Duality for massive spin two theories in arbitrary dimensions

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

On the degrees of freedom of R2 gravity in flat spacetime

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