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

We compute the renormalization group running of the Newton constant and the parameter λ in (3+1)-dimensional projectable Hořava 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 β-function of λ 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 β-functions for the rest of the couplings are added.