# Towards the renormalization group flow of Horava gravity in $(3+1)$ dimensions

## TL;DR

This paper investigates the renormalization group flow of key parameters in (3+1)-dimensional projectable Horava gravity, identifying potential fixed points that could inform the theory's behavior at different scales.

## Contribution

It provides the first calculation of the RG flow of Newton's constant and the parameter λ in (3+1)D Horava gravity using a simplified background field method.

## Key findings

- Beta function of λ has two zeros, indicating potential fixed points.
- Fixed points are attractive in both infrared and ultraviolet regimes.
- Simplified calculation method reduces complexity of RG flow analysis.

## Abstract

We compute the renormalization group running of the Newton constant and the parameter $\lambda$ in $(3+1)$-dimensional projectable Horava gravity. We use the background field method expanding around configurations with flat spatial metric, but non-vanishing shift. This allows us to reduce the number of interaction vertices and thereby drastically simplify the calculations. The gauge invariant $\beta$-function of $\lambda$ has two families of zeros, attractive in the infrared and ultraviolet respectively. They are candidates for the fixed points of the full renormalization group flow of the theory, once the $\beta$-functions for the rest of the couplings are added.