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

## TL;DR

This paper demonstrates that projectable Hořava gravity in 2+1 dimensions is asymptotically free in the UV, indicating it is a UV-complete quantum gravity model with potential as a simplified framework for studying quantum gravity.

## Contribution

It computes the beta functions of marginal couplings in 2+1D Hořava gravity and shows the existence of an asymptotically free fixed point, advancing understanding of its UV behavior.

## Key findings

- The beta functions indicate an asymptotically free fixed point in the UV.
- The theory is shown to be UV-complete with dynamical gravitational degrees of freedom.
- Results contribute to understanding the UV properties of Hořava gravity.

## Abstract

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.