Quantum-gravity effects on a Higgs-Yukawa model

Abstract

A phenomenologically viable theory of quantum gravity must accommodate all observed matter degrees of freedom and their properties. Here, we explore whether a toy model of the Higgs-Yukawa sector of the Standard Model is compatible with asymptotically safe quantum gravity. We discuss the phenomenological implications of our result in the context of the Standard Model.We analyze the quantum scaling dimension of the system, and find an irrelevant Yukawa coupling at a joint gravity-matter fixed point. Further, we explore the impact of gravity-induced couplings between scalars and fermions, which are non-vanishing in asymptotically safe gravity.

Upper bound on the Abelian gauge coupling from asymptotic safety

“…Physically, marginal irrelevance means a growth of the coupling towards the ultraviolet. Asymptotically safe quantum gravity adds a contribution to the beta function of all matter couplings that is linear in the matter coupling [1,16,[33][34][35][36][37][38][39][40][41][42][43][44][45][46]. If the sign of the gravitational contribution is negative, a fundamental change is triggered in the high-energy behavior of the corresponding coupling: the UV-repulsive free fixed point is turned into a UV attractive fixed point.…”

The β-function for Yukawa theory at large Nf

“…refs. [1][2][3]. In particular, gauge-Yukawa theories with a large number of fermion flavours, N f , provide interesting candidates within the asymptotic-safety framework as opposed to the traditional asymptotic-freedom paradigm [4,5].…”

Is scale-invariance in gauge-Yukawa systems compatible with the graviton?

“…(2.5). The direct contribution to the running of a simple Yukawa coupling has been evaluated in [54][55][56][57][58], including anomalous dimensions in [59]. Here, we have also derived the gravity contributions to the β-functions in the gauge and matter sector for general gauges (see appendix A), thus generalizing the results of [30] and [59].…”

“…It is intriguing to observe that the fixed-point structure of the gauge-Yukawa system at g > g crit appears to potentially be attainable at intermediate scales if one starts from an asymptotically safe matter-gravity model: There, studies indicate that the Yukawa coupling generically features a fixed point at α y = 0 [54][55][56][57][58][59]. Moreover, α N can feature a fixed point at which it is finite and IR-attrative [29], at least in the Abelian case.…”