Beta functions of (3+1)-dimensional projectable Hořava gravity

We derive the full set of beta functions for the marginal essential couplings of projectable Hořava gravity in (3+1)-dimensional spacetime. To this end we compute the divergent part of the one-loop effective action in static background with an arbitrary spatial metric. The computation is done in several steps: reduction of the problem to three dimensions, extraction of an operator square root from the spatial part of the fluctuation operator, …