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

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.

typos corrected; Accepted for publication in Class. and Quantum Grav.; 50 pages, 5 figures; typos corrected in Eqs. (61), (62), and (79); the last paragraph of Sec. 5.4 added; references added; other minor revisions