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.

中文翻译：

---

Hořava重力在2 + 1维中渐近自由

我们计算 $\beta$ 边缘联轴器在可投影Hořava重力中的作用。 $\mathrm{2个}+\mathrm{1个}$时空维度。我们表明，重归一化群流在紫外线（UV）中具有一个渐近自由的固定点，从而将该理论确立为具有动态重力自由度的UV完全模型。因此，该理论可以作为研究量子引力基本方面的玩具模型。我们的结果代表了朝着了解真实版本的霍瓦瓦引力的紫外线特性迈出的一步。