Ho\v{r}ava gravity is asymptotically free (in 2+1 dimensions)

Understand

We compute the $\beta$-functions of marginal couplings in projectable Ho\v{r}ava gravity in $2+1$ spacetime dimensions.

• We show that the renormalization group flow has an asymptotically-free fixed point in the ultraviolet (UV), establishing the theory as a UV-complete model with dynamical gravitational degrees of freedom.
• Therefore, this theory may serve as a toy-model to study fundamental aspects of quantum gravity.
• Our results represent a step forward towards understanding the UV properties of realistic versions of Ho\v{r}ava gravity.