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Quasi-Riemannian gravity and spontaneous breaking of the Lorentz gauge symmetry in more than four dimensions
Phys. Rev. D 33, 3594 – Published 15 June, 1986
DOI: https://doi.org/10.1103/PhysRevD.33.3594
Abstract
It is shown that a pure gravity theory in d dimensions, with an action quadratic in torsion and curvature, may lead to a spontaneous breaking of the SO(1,d-1) gauge symmetry. The physical vacuum, corresponding to a minimum of the self-interaction torsion potential, is characterized by a constant nonvanishing torsion background, and in the lowest-order expansion of the gravitational field around this configuration, an effective quasi-Riemannian theory is obtained. In particular, all nine parameters of the corresponding quasi-Riemannian action are determined, as a function of the torsion self-interaction coupling strength, for the tangent space groups SO(1,d-4)×SO(3) and SO(1,d-2). Finally, the possibility that a breaking of the local Lorentz symmetry may be associated to a change of sign of the effective four-dimensional gravitational coupling constant is discussed.
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