Infinite order quantum-gravitational correlations

TL;DR

This paper introduces a new approximation scheme for nonperturbative quantum gravity that enables studying correlation functions of any order by fully resolving the dependence on the graviton fluctuation field, advancing the understanding of quantum gravitational phases.

Contribution

It develops a novel method to analyze infinite-order quantum-gravitational correlations by extending the renormalisation group approach to include all couplings related to the graviton field.

Findings

Indications of a non-metric phase in deep ultraviolet quantum gravity.

Improved analysis of fluctuation vertices by including infinitely many couplings.

Progress towards resolving the Nielsen identity in quantum gravity.

Abstract

A new approximation scheme for nonperturbative renormalisation group equations for quantum gravity is introduced. Correlation functions of arbitrarily high order can be studied by resolving the full dependence of the renormalisation group equations on the fluctuation field (graviton). This is reminiscent of a local potential approximation in O(N)-symmetric field theories. As a first proof of principle, we derive the flow equation for the "graviton potential" induced by a conformal fluctuation and corrections induced by a gravitational wave fluctuation. Indications are found that quantum gravity might be in a non-metric phase in the deep ultraviolet. The present setup significantly improves the quality of previous fluctuation vertex studies by including infinitely many couplings, thereby testing the reliability of schemes to identify different couplings to close the equations, and represents an important step towards the resolution of the Nielsen identity. The setup further allows in principle to address the question of putative gravitational condensates.