Linear connections with a propagating spin-3 field in gravity

Baekler, Peter; Boulanger, Nicolas; Hehl, Friedrich W.

doi:10.1103/physrevd.74.125009

Cited by 23 publications

(34 citation statements)

References 54 publications

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“…Also of some interest would be the study of models with propagating spin 3 − . It is known that the free massless spin 3 theory can be embedded in linearized MAG [46], however the underlying linearized gauge symmetry does not extend to the full theory. It would be interesting to explore whether MAG can describe a massive spin 3 field coupled to gravity.…”

Section: Discussionmentioning

confidence: 99%

New class of ghost- and tachyon-free metric affine gravities

2020

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We construct the spin-projection operators for a theory containing a symmetric two-index tensor and a general three-index tensor. We then use them to analyse, at linearized level, the most general action for a metric-affine theory of gravity with terms up to second order in curvature, which depends on 28 parameters. In the metric case we recover known results. In the torsion-free case, we are able to determine the most general six-parameter class of theories that are projective invariant, contain only one massless spin 2 and no spin 3, and are free of ghosts and tachyons.1 By quadratic gravity we mean theories with action containing terms linear and quadratic in the Riemann tensor.2 As an example let us mention here Weyl geometry, where φ is constructed in terms of a vector field. This theory has been revisited recently in [27].3 By accidental symmetry we mean a gauge symmetry that is present in the linearized action but not in the full action 4 This is due to the use of the vierbein formalism. The general two-index tensor is the linearized vierbein and the three-index tensor is the linearized spin connection.

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Section: Discussionmentioning

confidence: 99%

New class of ghost- and tachyon-free metric affine gravities

2020

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“…In particular, it would be interesting to generalize the construction of [71] concerning the Chern-Simons formulation of threedimensional gravity involving torsion and nonmetricity, and the recent results presented in [88] in the context of double field theory. One could also investigate possible generalizations of [85,86].…”

Section: Discussionmentioning

confidence: 99%

“…In the following we extend the above analysis to include a traceless part of the nonmetricity as well. Interestingly, in the case where the latter is totally symmetric, it can be viewed as representing a massless spin-3 field [85,86].…”

Section: Adding a Traceless Part To The Nonmetricity Tensormentioning

confidence: 99%

Einstein manifolds with torsion and nonmetricity

Klemm

Ravera

2020

Phys. Rev. D

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Manifolds endowed with torsion and nonmetricity are interesting both from the physical and the mathematical points of view. In this paper, we generalize some results presented in the literature. We study Einstein manifolds in d dimensions with nonvanishing torsion that has both a trace and a traceless part, and analyze the conformal invariance of the corresponding field equations. Then, we compare our results to the case of Einstein manifolds with zero torsion and nonvanishing nonmetricity, where the latter is given in terms of the Weyl vector (Einstein-Weyl spaces). We find that the trace part of the torsion can alternatively be interpreted as the trace part of the nonmetricity. The analysis is subsequently extended to Einstein spaces with both torsion and nonmetricity, where we also discuss the general setting in which the nonmetricity tensor has both a trace and a traceless part. Moreover, we consider and investigate actions involving scalar curvatures obtained from torsionful or nonmetric connections, analyzing their relations with other gravitational theories that appeared previously in the literature. In particular, we show that the Einstein-Cartan action and the scale invariant gravity (i.e., conformal gravity) action describe the same dynamics. Then, we consider the Einstein-Hilbert action coupled to a three-form field strength and shew that its equations of motion imply that the manifold is Einstein with skew-symmetric torsion.In the 19th century, the branches of mathematics and physics experienced an extraordinary progress with the emergence of non-Euclidean geometry. In particular, the development of Riemannian geometry led to many important results, among which the rigorous mathematical formulation of Einstein's general relativity.In spite of the success and predictive power of general relativity, there are still some open problems and questions, whose understanding and solution may need the formulation of a new theoretical framework as well as generalizations and extensions of Riemannian geometry. One possible way of generalizing Riemannian geometry consists in allowing for nonvanishing torsion and nonmetricity (metric affine gravity) [1] (see also [2] and the recent work [3]). There are several physical (and mathematical) reasons which motivate the introduction of torsion or nonmetricity in the context of gravitational theories (see [1] for details). For instance, nonmetricity is a measure for the violation of local Lorentz invariance, which has been attracting some interest recently. Furthermore, nonmetricity and torsion find applications in the theory of defects in crystals, where, in particular, nonmetricity describes the density of point defects, while torsion is interpreted as density in line defects [4]. Moreover, as recently shown in [5], incorporating torsion and nonmetricity may allow to explore new physics associated with defects in a hypothetical spacetime microstructure. Further applications include quantum gravity [6] and cosmology [7][8][9].Historically, a remarkable generalization of ...

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“…Additional gauge fields that describe the non-Riemannian part of a connection have been considered in analysis of metric affine gravity models (see [9], Sec. 3.11; [10]); the earliest example of a connection modified by an abelian gauge field is the Weyl connection [11]. From these considerations it follows that one can use the one-forms A ab = A ab µ dx µ by formally extending the Riemannian connection ω ab = ω ab µ dx µ to non-Riemannian one with torsion…”

Section: Introductionmentioning

confidence: 99%

Generalized cosmological term from Maxwell symmetries

2011

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By gauging the Maxwell spacetime algebra the standard geometric framework of Einstein gravity with cosmological constant term is extended by adding six fourvector fields A_\mu^{ab}(x) associated with the six abelian tensorial charges in the Maxwell algebra. In the simplest Maxwell extension of Einstein gravity this leads to a generalized cosmological term that includes a contribution from these vector fields. We also consider going beyond the basic gravitational model by means of bilinear actions for the new Abelian gauge fields. Finally, an analogy with the supersymmetric generalization of gravity is indicated. In an Appendix, we propose an equivalent description of the model in terms of a shift of the standard spin connection by the A_\mu^{ab}(x) fields.Comment: 7 pages, RevTex style. Enlarged version to appear in PR

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Linear connections with a propagating spin-3 field in gravity

Cited by 23 publications

References 54 publications

New class of ghost- and tachyon-free metric affine gravities

New class of ghost- and tachyon-free metric affine gravities

Einstein manifolds with torsion and nonmetricity

Generalized cosmological term from Maxwell symmetries

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