RG flow of projectable Horava gravity in (3+1)d

We report a comprehensive numerical study of the renormalization group flow of marginal couplings in (3+1)-dimensional projectable Horava gravity. First, we classify all fixed points of the flow and analyze their stability matrices. Next, we identify a unique fixed point giving rise to a set of trajectories spanning the whole range of the kinetic coupling λ compatible with unitarity. This includes the region 0<λ-1<<1 assumed in previous phenomenological applications. The respective trajectories closely follow a single universal trajectory, differing only by the running of the gravitational coupling. The latter exhibits nonmonotonic behavior along the flow, vanishing both in the ultraviolet and the infrared limits. The requirement that the theory remains weakly coupled along the renormalization group trajectory implies a natural hierarchy between the scale of Lorentz invariance violation and a much larger value of the Planck mass inferred from low-energy interactions.