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

## TL;DR

This paper investigates how quantum gravity influences fixed points in gauge-Yukawa systems, revealing that gravity can modify scaling dimensions and induce effective dimensional reduction, impacting the systems' fixed-point structure and stability.

## Contribution

It demonstrates that quantum gravity effects preserve and alter fixed points in gauge-Yukawa systems, introducing effective dimensional reduction and new fixed points.

## Key findings

- Quantum gravity preserves fixed points in gauge theories.
- Gravity induces effective dimensional reduction in matter systems.
- New partially interacting fixed points emerge due to graviton effects.

## Abstract

We explore whether perturbative interacting fixed points in matter systems can persist under the impact of quantum gravity. We first focus on semi-simple gauge theories and show that the leading order gravity contribution evaluated within the functional Renormalization Group framework preserves the perturbative fixed-point structure in these models discovered in [1]. We highlight that the quantum-gravity contribution alters the scaling dimension of the gauge coupling, such that the system exhibits an effective dimensional reduction. We secondly explore the effect of metric fluctuations on asymptotically safe gauge-Yukawa systems which feature an asymptotically safe fixed point [2]. The same effective dimensional reduction that takes effect in pure gauge theories also impacts gauge-Yukawa systems. There, it appears to lead to a split of the degenerate free fixed point into an interacting infrared attractive fixed point and a partially ultraviolet attractive free fixed point. The quantum-gravity induced infrared fixed point moves towards the asymptotically safe fixed point of the matter system, and annihilates it at a critical value of the gravity coupling. Even after that fixed-point annihilation, graviton effects leave behind new partially interacting fixed points for the matter sector.