  We derive the full set of beta functions for the marginal essential couplings
of projectable Horava gravity in (3 + 1)-dimensional spacetime. To this end we
compute the divergent part of the one-loop effective action in static
background with 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, and evaluation
of its trace using the method of universal functional traces. This provides us
with the renormalization of couplings in the potential part of the action which
we combine with the results for the kinetic part obtained previously. The
calculation uses symbolic computer algebra and is performed in four different
gauges yielding identical results for the essential beta functions. We
additionally check the calculation by evaluating the effective action on a
special background with spherical spatial slices using an alternative method of
spectral summation. We conclude with a preliminary discussion of the properties
of the beta functions and the resulting renormalization group flow, identifying
several candidate asymptotically free fixed points.
