Duality for symmetric second rank tensors. II. The linearized gravitational field

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

doi:10.1103/physrevd.68.065011

Cited by 37 publications

(52 citation statements)

References 28 publications

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“…This type of models became of special interest lately due to the many desirable featured exhibited, like the dual formulation of field theories of spin two or higher [7,8,9,10,11,12], the impossibility of consistent cross-interactions in the dual formulation of linearized gravity [13] or a Lagrangian first-order approach [14,15] to some classes of massless or partially massive mixed symmetry-type tensor gauge fields, suggestively resembling to the tetrad formalism of General Relativity. A basic problem involving mixed symmetrytype tensor fields is the approach to their local BRST cohomology, since it is helpful at solving many Lagrangian and Hamiltonian aspects, like, for instance the determination of their consistent interactions [16] with higher-spin gauge theories [6,18,19,20,21,22,30,31].…”

Section: Introductionmentioning

confidence: 99%

COHOMOLOGICAL BRST ASPECTS OF THE MASSLESS TENSOR FIELD WITH THE MIXED SYMMETRY (k,k)

Ciobirca

Cioroianu

Saliu

2004

Int. J. Mod. Phys. A

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The main BRST cohomological properties of a free, massless tensor field that transforms in an irreducible representation of GL (D, R), corresponding to a rectangular, two-column Young diagram with k > 2 rows are studied in detail. In particular, it is shown that any nontrivial co-cycle from the local BRST cohomology group H (s|d) can be taken to stop either at antighost number (k + 1) or k, its last component belonging to the cohomology of the exterior longitudinal derivative H (γ) and containing non-trivial elements from the (invariant) characteristic cohomology H inv (δ|d).

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Section: Introductionmentioning

confidence: 99%

COHOMOLOGICAL BRST ASPECTS OF THE MASSLESS TENSOR FIELD WITH THE MIXED SYMMETRY (k,k)

Ciobirca

Cioroianu

Saliu

2004

Int. J. Mod. Phys. A

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“…At the linearized level, a Schwarzschild metric g with mass m is dual to a Taub-NUT metric g with NUT parameter ℓ = m (and mass m = 0) [3,4]. However, this simple relation does not continue to hold at the full nonlinear level, since a metric g( m, ℓ)…”

Section: Introductionmentioning

confidence: 99%

“…The properties of R abcd have previously been discussed in [3][4][5][6]. [18] (the distinction between latin and greek indices is meaningless at the linearized level) as…”

Section: The Dual Of Gravitymentioning

confidence: 99%

“…At the level of linearized standard gravitational S-duality, the parameters m and ℓ of a Taub-NUT metric [19,20] get interchanged [3,4]. Hence the NUT parameter ℓ can be interpreted as a "magnetic" mass.…”

Section: Non-standard Duality and Taub-nut-(a)ds Spacesmentioning

confidence: 99%

“…Subsequently we confine ourselves to d = 4 dimensions, where the dual of a graviton is again a graviton-like symmetric two-component tensor field [2][3][4][5][6]. We want to persue the question whether a metric obtained through such a duality transformation can describe naturally a space time which is flat (rather than (A)dS), although the original space time (before the duality transformation) is (A)dS with arbitrary cosmological constant.…”

Section: Introductionmentioning

confidence: 99%

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Generalized gravitational S -duality and the cosmological constant problem

Ellwanger¹

2005

Class. Quantum Grav.

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We study S-duality transformations that mix the Riemann tensor with the field strength of a 3-form field. The dual of an (A)dS space time -with arbitrary curvature -is seen to be flat Minkowski space time, if the 3-form field has vanishing field strength before the duality transformation. It is discussed whether matter could couple to the dual metric, related to the Riemann tensor after a duality transformation. This possibility is supported by the facts that the Schwarzschild metric can be obtained as a suitable contraction of the dual of a Taub-NUT-AdS metric, and that metrics describing FRW cosmologies can be obtained as duals of theories with matter in the form of torsion.

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Dual linearized gravity in D = 6 coupled to a purely spin‐two field of mixed symmetry (2,2)

Bizdadea¹,

Cioroianu

Saliu

et al. 2010

Fortschritte der Physik

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Under the hypotheses of analyticity, locality, Lorentz covariance, and Poincaré invariance of the deformations, combined with the requirement that the interaction vertices contain at most two spatiotemporal derivatives of the fields, we investigate the consistent interactions between a single massless tensor field with the mixed symmetry (3, 1) and one massless tensor field with the mixed symmetry (2, 2). The computations are done with the help of the deformation theory based on a cohomological approach, in the context of the antifield-BRST formalism. Our result is that dual linearized gravity in D = 6 gets coupled to a purely spin-two field with the mixed symmetry of the Riemann tensor such that both the gauge transformations and first-order reducibility relations in the (3, 1) sector are changed, but not the gauge algebra.Our analysis relies on the deformation of the solution to the master equation by means of cohomological techniques with the help of the local BRST cohomology, whose component in the (3, 1) sector has been reported in detail in [26] and in the (2, 2) sector has been investigated in [27,28]. Apart from the duality of the massless tensor field with the mixed symmetry (3, 1) to the Pauli-Fierz theory (linearized limit of Einstein-Hilbert gravity) in D = 6 dimensions, it is interesting to mention the developments concerning the dual formulations of linearized gravity from the perspective of M -theory [29]- [31]. On the other hand, the massless tensor field with the mixed symmetry (2, 2) displays all the algebraic properties of the Riemann tensor, describes purely spin-two particles, and also provides a dual formulation of linearized gravity in D = 5. Actually, there is a revived interest in the construction of dual gravity theories, which led to several new results, viz. a dual formulation of linearized gravity in first order tetrad formalism in arbitrary dimensions within the path integral framework [32] or a reformulation of non-linear Einstein gravity in terms of the dual graviton together with the ordinary metric and a shift gauge field [33].Under the hypotheses of analyticity, locality, Lorentz covariance, and Poincaré invariance of the deformations, combined with the requirement that the interaction vertices contain at most two spatiotemporal derivatives of the fields, we prove that there exists a case where the deformation of the solution to the master equation provides non-trivial cross-couplings. This case corresponds to a six-dimensional spacetime and is described by a deformed solution that stops at order two in the coupling constant. In this way we establish a new result, namely that dual linearized gravity in D = 6 gets coupled to a purely spin-two field with the mixed symmetry of the Riemann tensor. The interacting Lagrangian action contains only mixingcomponent terms of order one and two in the coupling constant. This is the first time when both the gauge transformations and first-order reducibility functions of the tensor field (3, 1) are modified at order one in the coupling consta...

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Duality for symmetric second rank tensors. II. The linearized gravitational field

Cited by 37 publications

References 28 publications

COHOMOLOGICAL BRST ASPECTS OF THE MASSLESS TENSOR FIELD WITH THE MIXED SYMMETRY (k,k)

COHOMOLOGICAL BRST ASPECTS OF THE MASSLESS TENSOR FIELD WITH THE MIXED SYMMETRY (k,k)

Generalized gravitational S -duality and the cosmological constant problem

Dual linearized gravity in D = 6 coupled to a purely spin‐two field of mixed symmetry (2,2)

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