Asymptotic freedom in (3+1)-dimensional projectable Hořava gravity: Connecting the ultraviolet and infrared domains

We investigate the renormalization group flow of projectable Hořava gravity in (3+1) dimensions generated by marginal operators with respect to the Lifshitz scaling. The flow possesses a number of asymptotically free fixed points. We find a family of trajectories connecting one of these fixed points in the ultraviolet to the region of the parameter space where the kinetic term of the theory acquires the general relativistic form. The gravitational coupling exhibits nonmonotonic behavior along the flow, vanishing both in the ultraviolet and the infrared.