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On unitarity of a linearized Yang-Mills formulation for massless and massive gravity with propagating torsion
A perturbative regime based on contortion as a dynamical variable and metric
as a (classical) fixed background, is performed in the context of a pure
Yang-Mills formulation for gravity in a dimensional space-time. In the
massless case we show that the theory contains three degrees of freedom and
only one is a non-unitary mode. Next, we introduce quadratical terms dependent
on torsion, which preserve parity and general covariance. The linearized
version reproduces an analogue Hilbert-Einstein-Fierz-Pauli unitary massive
theory plus three massless modes, two of them represents non-unitary ones.
Finally we confirm the existence of a family of unitary Yang-Mills-extended
theories which are classically consistent with Einstein's solutions coming from
non massive and topologically massive gravity. The unitarity of these
YM-extended theories is shown in a perturbative regime. A possible way to
perform a non-perturbative study is remarked.Comment: To appear in International Journal of Modern Physics
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