Effective matter dispersion relation in quantum covariant Horava-Lifshitz gravity

Abstract

We study how quantum fluctuations of the metric in covariant Hořava-Lifshitz gravity influence the propagation of classical fields (complex scalar and photon). The effective Lorentz-symmetry violation induced by the breaking of 4-dimensional diffeomorphism is then evaluated, by comparing the dressed dispersion relations for both external fields. The constraint of vanishing 3-dimensional Ricci scalar is imposed in the path integral, which therefore explicitly depends on two propagating gravitational degrees of freedom only. Because the matter fields are classical, the present model contains only logarithmic divergences. Furthermore, it imposes the characteristic Hořava-Lifshitz scale to be smaller than 10 10 GeV, if one wishes not to violate the current bounds on Lorentz symmetry violation.

Effective fermion kinematics from modified quantum gravity

“…The same characteristic scale is also found in [21], where non-relativistic corrections to matter kinetic terms are calculated in the framework of the Covariant HL gravity [22]. We note that this scale also corresponds to the Higgs potential instability [23], which could be avoided by taking into account curvature effects in the calculation of the Higgs potential [24].…”

Covariant computation of effective actions in Hořava-Lifshitz gravity

“…This feature makes HL gravity power-counting renormalizable and constitutes an important (though not sufficient) ingredient for the theory being asymptotically free at the anisotropic Gaussian fixed point (aGFP). The quantum properties of HL gravity beyond power-counting arguments have recently been investigated analytically [10][11][12][13][14] as well as within Monte Carlo simulations based on Causal Dynamical Triangulations [15][16][17][18].…”