Non-minimal coupling in Higgs-Yukawa model with asymptotically safe gravity

TL;DR

This paper investigates the fixed point structure of the Higgs-Yukawa model with non-minimal coupling to asymptotically safe gravity using the functional renormalization group, revealing the irrelevance of the non-minimal coupling when fermionic fluctuations are included.

Contribution

It provides a detailed analysis of the RG flow of the Higgs-Yukawa model with non-minimal coupling in the context of asymptotically safe gravity, including all relevant quantum loops.

Findings

Fermionic quantum fluctuations render the non-minimal coupling irrelevant.

Derived RG equations for key couplings in the model.

Identified fixed point structure consistent with asymptotic safety.

Abstract

We study the fixed point structure of the Higgs-Yukawa model, with its scalar being non-minimally coupled to the asymptotically safe gravity, using the functional renormalization group. We have obtained the renormalization group equations for the cosmological and Newton constants, the scalar mass-squared and quartic coupling constant, and the Yukawa and non-minimal coupling constants, taking into account all the scalar, fermion, and graviton loops. We find that switching on the fermionic quantum fluctuations makes the non-minimal coupling constant irrelevant around the Gaussian-matter fixed point with the asymptotically safe gravity.