Quasi-Riemannian gravity and spontaneous breaking of the Lorentz gauge symmetry in more than four dimensions.

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) x 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.