Discussion on massive gravitons and propagating torsion in arbitrary dimensions

C. A. Hernaski, A. A. Vargas-Paredes†, J. A. Helay¨el-Neto‡

Centro Brasileiro de Pesquisas F´?sicas,

Rua Dr. Xavier Sigaud 150, Urca,

Rio de Janeiro, Brazil, CEP 22290-180

*"In this paper, we reassess a particular R2-type gravity action in D dimensions, recently studied by Nakasone and Oda, now taking torsion effects into account. Considering that the vielbein and the spin connection carry independent propagating degrees of freedom, we conclude that ghosts and tachyons are absent only if torsion is nonpropagating, and we also conclude that there is no room for massive gravitons. To include these excitations, we understand how to enlarge Nakasone-Oda’s model by means of explicit torsion terms in the action and we discuss the unitarity of the enlarged*

model for arbitrary dimensions."
I think the opposite should be considered, i.e. real on shell ghosts violating spin-statistics and real tachyons with propagating torsion waves.

*"the graviton acquires mass via a spontaneous breakdown of general coordinate reparametrization symmetry ... massive gravitons is drawing a great deal of attention, in view of the possibility of their production at LHC and the feasibility of detection of quantum gravity effects at the TeV scale ... as it is usual in all Higgs-type mechanisms, a nonvanishing vacuum expectation value for an extra scalar field is needed in the description. There is also an alternative way to generate mass in three dimensions, as proposed by Jackiw, Deser and Templeton [7]. There, a topological parity-violating term is added to the Einstein-Hilbert gravity Lagrangian in order to describe a massive graviton. The final theory is also unitary ...*

we asked if it is possible to build up a unitarity and parity-preserving model that generates mass for the graviton without the need of an extra field. Bergshoeff, Hohm and Townsend obtain such a model for D = 3 [8] by considering a nonlinear theory that is equivalent to the Pauli-Fierz model at the linear level. ... Three-dimensional gravity has no local degrees of freedom. The Riemann tensor has the same number of components as the Ricci tensor, which means that all solutions in these theories are trivial, with the exception of those that consider topological effects. However, the situation might change if we consider massive spin-2 propagating modes in three dimensions. ...*We work with the vielbein* (aka tetrad)

*and the spin connection as independent fields. Our viewpoint is that this is a more fundamental approach to gravitation, since it is based on the fundamental ideas of the Yang-Mills approach"*
Exactly, this is from localizing the 10-parameter global Poincare group of 1905 SR.

*"explicit terms in the torsion field are needed in order to describe a propagating massive graviton."*
(Note I use (4) in my emergent gravity model from the 8 post-inflation Goldstone vacuum phases via what I call the "M-Matrix" of Cartan 1-forms)

*"our model is invariant under linearized general coordinates and local Lorentz transformations. ... for a massive propagating particle not to be a tachyon or a ghost, we must require that ..."*
This may be an erroneous assumption in my opinion. I am not loath to consider the possibility that unitarity may not be preserved under all conditions and that there are not on-mass-shell real ghost and tachyonic particles. Note that ghosts have "wrong" spin-statistics and tachyons are thought to induce vacuum instabilities.