In (3+1)-dimensional projectable Horava gravity, a unique ultraviolet fixed point produces renormalization group trajectories covering the entire unitary range of the kinetic coupling and predicts a large hierarchy between the Planck mass and the Lorentz violation scale.
Relativistic Quantum Gravity at a Lifshitz Point
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abstract
We show that the Horava theory for the completion of General Relativity at UV scales can be interpreted as a gauge fixed theory, and it can be extended to an invariant theory under the full group of four-dimensional diffeomorphisms. In this respect, although being fully relativistic, it results to be locally anisotropic in the time-like and space-like directions defined by a family of irrotational observers. We show that this theory propagates generically three degrees of freedom: two of them are related to the four-dimensional diffeomorphism invariant graviton (the metric) and one is related to a propagating scalar mode. Finally, we note that in the present formulation, matter can be consistently coupled to gravity.
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Renormalization group flow of projectable Ho\v{r}ava gravity in (3+1) dimensions
In (3+1)-dimensional projectable Horava gravity, a unique ultraviolet fixed point produces renormalization group trajectories covering the entire unitary range of the kinetic coupling and predicts a large hierarchy between the Planck mass and the Lorentz violation scale.