Towards the renormalization group flow of Horava gravity in 3+1 dimensions

We compute the renormalization group running of the Newton constant and the parameter lambda in (3 + 1)-dimensional projectable Horava gravity. We use the background-field method, expanding around configurations with flat spatial metric, but nonvanishing shift. This allows us to reduce the number of interaction vertices and thereby drastically simplify the calculations. The gauge-invariant beta-function of. has two families of zeros, attractive in the infrared and ultraviolet, respectively. They are candidates for the fixed points of the full renormalization group flow of the theory, once the beta-functions for the rest of the couplings are added.