Renormalization Group Flow of Quantum Gravity in the Einstein-Hilbert Truncation

TL;DR

This paper investigates the non-perturbative renormalization group flow of quantum gravity within the Einstein-Hilbert truncation, identifying fixed points that could imply nonperturbative renormalizability of Quantum Einstein Gravity.

Contribution

It derives and analyzes the non-perturbative beta functions for quantum gravity using the exact renormalization group equation with a sharp cutoff, providing new insights into the flow and fixed points.

Findings

Identification of the non-trivial fixed point in 4 dimensions.

Complete classification of renormalization group trajectories.

Comparison of flow features between sharp and smooth cutoff functions.

Abstract

The exact renormalization group equation for pure quantum gravity is used to derive the non-perturbative $\Fbeta$-functions for the dimensionless Newton constant and cosmological constant on the theory space spanned by the Einstein-Hilbert truncation. The resulting coupled differential equations are evaluated for a sharp cutoff function. The features of these flow equations are compared to those found when using a smooth cutoff. The system of equations with sharp cutoff is then solved numerically, deriving the complete renormalization group flow of the Einstein-Hilbert truncation in $d=4$. The resulting renormalization group trajectories are classified and their physical relevance is discussed. The non-trivial fixed point which, if present in the exact theory, might render Quantum Einstein Gravity nonperturbatively renormalizable is investigated for various spacetime dimensionalities.