Asymptotic freedom in Horava-Lifshitz gravity

TL;DR

This paper demonstrates that projectable Horava-Lifshitz gravity coupled with multiple scalars is asymptotically free due to an ultraviolet fixed point, suggesting its perturbative renormalizability.

Contribution

It provides explicit beta functions for the gravitational couplings using novel anisotropic heat kernel techniques, showing asymptotic freedom in the large-n limit.

Findings

Existence of an UV attractive anisotropic Gaussian fixed point

Newton's constant vanishes at the fixed point

Theory is perturbatively renormalizable

Abstract

We use the Wetterich equation for foliated spacetimes to study the RG flow of projectable Horava-Lifshitz gravity coupled to n Lifshitz scalars. Using novel results for anisotropic heat kernels, the matter-induced beta functions for the gravitational couplings are computed explicitly. The RG flow exhibits an UV attractive anisotropic Gaussian fixed point where Newton's constant vanishes and the extra scalar mode decouples. This fixed point ensures that the theory is asymptotically free in the large-n expansion, indicating that projectable Horava-Lifshitz gravity is perturbatively renormalizable. Notably, the fundamental fixed point action does not obey detailed balance.