Towards apparent convergence in asymptotically safe quantum gravity

TL;DR

This paper advances the understanding of asymptotically safe quantum gravity by extending the vertex expansion scheme to include the graviton four-point function, revealing a UV fixed point and signs of convergence.

Contribution

The work introduces a closed flow equation for the graviton propagator within the vertex expansion scheme, enabling systematic inclusion of higher-order operators in quantum gravity.

Findings

Identified a UV fixed point with three attractive and two repulsive directions.

Found trajectories in the IR corresponding to classical general relativity.

Provided evidence for the apparent convergence of the systematic vertex expansion.

Abstract

The asymptotic safety scenario in gravity is accessed within the systematic vertex expansion scheme for functional renormalisation group flows put forward in \cite{Christiansen:2012rx,Christiansen:2014raa}, and implemented in \cite{Christiansen:2015rva} for propagators and three-point functions. In the present work this expansion scheme is extended to the dynamical graviton four-point function. For the first time, this provides us with a closed flow equation for the graviton propagator: all vertices and propagators involved are computed from their own flows. In terms of a covariant operator expansion the current approximation gives access to $\Lambda$, $R$, $R^2$ as well as $R_{\mu\nu}^2$ and higher derivative operators. We find a UV fixed point with three attractive and two repulsive directions, thus confirming previous studies on the relevance of the first three operators. In the infrared we find trajectories that correspond to classical general relativity and further show non-classical behaviour in some fluctuation couplings. We also find signatures for the apparent convergence of the systematic vertex expansion. This opens a promising path towards establishing asymptotically safe gravity in terms of apparent convergence.