---
abstract: 'We investigate the non-perturbative renormalization group behavior of the gauge coupling constant using a truncated form of the functional flow equation for the effective average action of the Yang-Mills–gravity system. We find a non-zero quantum gravity correction to the standard Yang-Mills beta function which has the same sign as the gauge boson contribution. Our results fit into the picture according to which Quantum Einstein Gravity (QEG) is asymptotically safe, with a vanishing gauge coupling constant at the non-trivial fixed point.'
author:
- |
    J.-E. Daum, U. Harst and M. Reuter\
    [Institute of Physics, University of Mainz]{}\
    [Staudingerweg 7, D-55099 Mainz, Germany]{}
title: |
    Running Gauge Coupling in\
    Asymptotically Safe Quantum Gravity
---

Introduction
============

Recently a lot of efforts went into the computation of gravitational corrections to the beta function of the running Yang-Mills coupling constant. Robinson and Wilczek [@ymg-robwil; @ymg-robthesis], in an effective field theory setting, obtained a non-zero correction at the one-loop level. It has the same negative sign as the familiar term already present in absence of gravity, and so it would render even pure abelian theories asymptotically free. After Pietrykowski [@ymg-piet] had realized that this result is gauge fixing dependent, Toms [@ymg-toms] reanalyzed the 