Hořava Gravity is Asymptotically Free in $2+1$ Dimensions

We compute the $\beta$ functions of marginal couplings in projectable Hořava 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 Hořava gravity.

Figure 1

Feynman diagrams (bubbles and fishes) for the two point function of $H_{ij}$. The cross represents the mixed propagator $⟨n^i{\pi }^j⟩$.

Figure 2

RG flow of the couplings in ($2+1$)-dimensional Hořava gravity. The arrows show the direction of the flow towards the infrared.