The conformal sector of Quantum Einstein Gravity beyond the local potential approximation

TL;DR

This paper investigates the conformal sector of Quantum Einstein Gravity beyond the local potential approximation, revealing a complex structure of fixed points and eigenoperators influenced by the anomalous dimension of Newton's constant.

Contribution

It introduces a detailed analysis of the conformally reduced Einstein-Hilbert action, uncovering a line of fixed points and a spectrum of eigenoperators dependent on the anomalous dimension.

Findings

Identification of a line of fixed points characterized by the anomalous dimension.

Discovery of three distinct ranges of the anomalous dimension with different properties.

Finite dimensionality of the ultraviolet critical manifold for certain anomalous dimensions.

Abstract

The anomalous scaling of Newton's constant around the Reuter fixed point is dynamically computed using the functional flow equation approach. Specifically, we thoroughly analyze the flow of the most general conformally reduced Einstein-Hilbert action. Our findings reveal that, due to the distinctive nature of gravity, the anomalous dimension $\eta$ of the Newton's constant cannot be constrained to have one single value: the ultraviolet critical manifold is characterized by a line of fixed points $(g_\ast(\eta), \lambda_\ast (\eta))$, with a discrete (infinite) set of eigenoperators associated to each fixed point. More specifically, we find three ranges of $\eta$ corresponding to different properties of both fixed points and eigenoperators and, in particular, the range $ \eta < \eta_c \approx 0.96$ the ultraviolet critical manifolds has finite dimensionality.