# Asymptotic safety of higher derivative quantum gravity non-minimally coupled with a matter system

## TL;DR

This paper investigates the asymptotic safety of higher derivative quantum gravity models, with and without matter, using the functional renormalization group to identify fixed points and analyze the relevance of various couplings.

## Contribution

It derives beta functions for higher derivative quantum gravity with matter and finds non-trivial fixed points, highlighting the relevance of couplings in the gravity and matter sectors.

## Key findings

- All gravity couplings are relevant in pure higher derivative gravity.
- A stable fixed point exists for gravity coupled with matter, with relevant scalar and Yukawa couplings.
- The Yukawa coupling's relevance is key for finite Yukawa couplings in the Standard Model.

## Abstract

We study asymptotic safety of models of the higher derivative quantum gravity with and without matter. The beta functions are derived by utilizing the functional renormalization group, and non-trivial fixed points are found. It turns out that all couplings in gravity sector, namely the cosmological constant, the Newton constant, and the $R^2$ and $R_{\mu\nu}^2$ coupling constants, are relevant in case of higher derivative pure gravity. For the Higgs-Yukawa model non-minimal coupled with higher derivative gravity, we find a stable fixed point at which the scalar-quartic and the Yukawa coupling constants become relevant. The relevant Yukawa coupling is crucial to realize the finite value of the Yukawa coupling constants in the standard model.