Counterterms in semiclassical Horava-Lifshitz gravity

Understand

We analyze the semiclassical Ho\v{r}ava-Lifshitz gravity for quantum scalar fields in 3+1 dimensions.

• The renormalizability of the theory requires that the action of the scalar field contains terms with six spatial derivatives of the field, i.e.
• in the UV, the classical action of the scalar field should preserve the anisotropic scaling symmetry ($t \to L^{2z}t,$ $\vec{x} \to L^2 \vec{x}$, with $z=3$) of the gravitational action.
• We discuss the renormalization procedure based on adiabatic subtraction and dimensional regularization in the weak field approximation.