Yukawa interactions in Quantum Gravity

TL;DR

This work addresses whether nonzero Yukawa couplings can be reconciled with an asymptotically safe quantum gravity UV completion by performing a complete next-to-leading order FRG analysis that includes the full set of higher-order operators. It identifies two mechanisms by which higher-order operators influence the Yukawa sector and demonstrates a gravity-induced anti-screening of Yukawa interactions, enabling finite Yukawa couplings to emerge in the IR from an asymptotically free UV fixed point. The study finds an interacting gravity–matter fixed point with three relevant directions, and at NLO the Yukawa critical exponent is positive for both minimal and SM-like matter content: $\Theta_{y,\mathrm{MM}}=3.1^{+1.8}_{-1.1}$ and $\Theta_{y,\mathrm{SM}}=2.2^{+1.3}_{-1.0}$, implying Yukawas are generated in the IR. A novel NNLO uncertainty estimation via random stability-matrix entries supports the robustness of the result, indicating that nonvanishing Yukawas are compatible with asymptotically safe gravity and could underpin the SM’s UV completion. This lays groundwork for extending the analysis to all SM couplings in the same FRG framework.

Abstract

We present the first complete next-to-leading-order analysis of a Yukawa system within the framework of asymptotically safe quantum gravity. Our results are obtained through a systematic resummation of higher-order operators, revealing two distinct resummation mechanisms -- one of which has not been explored previously. In addition, we introduce a novel approach to estimate systematic uncertainties by simulating the impact of neglected higher-order contributions. We demonstrate that quantum gravity fluctuations anti-screen Yukawa interactions, thereby resolving previously inconclusive leading-order results. This anti-screening mechanism enables the generation of finite interactions from an asymptotically free Yukawa fixed point. Consequently, our findings provide strong evidence that non-vanishing Yukawa couplings are compatible with asymptotically safe quantum gravity, which is a necessary requirement for the Standard Model to emerge from an asymptotically safe ultraviolet completion.

Figures (3)

• Figure 1: We show the diagrammatic flow of the Yukawa coupling. At LO, all vertices and propagators are given by their tree-level expressions. For NLO, we include the flow equations of all vertices and propagators that appear in the LO flow of the Yukawa coupling and the scalar and fermion propagators.
• Figure 2: We show the regions in the $g$-$\lambda$ plane where $\Theta_y>0$ (green) and $\Theta_y<0$ (red) together with the location of the UV fixed point for $N_\text{f}=N_\text{s}=1$ (left) and for SM matter content (right) at NLO. The hashed region is the estimated error by simulating the impact of an NNLO contribution. In the grey region above the dashed line, at least one anomalous dimension is large, $\eta >2$. The asymptotically safe fixed point is located in the green region with a relevant Yukawa coupling.
• Figure 3: We show the critical exponents of the Yukawa couplings with error estimates as a function of the Newton coupling at $\lambda=\lambda^*$ for $N_\text{f}=N_\text{s}=1$ (left) and for SM matter content (right).