Proper Time Flow Equation for Gravity

TL;DR

This paper investigates a proper time renormalization group equation for Quantum Einstein Gravity, demonstrating its consistency with the effective average action approach and confirming the existence of a non-Gaussian fixed point crucial for nonperturbative renormalizability.

Contribution

It introduces and analyzes a proper time RG equation for Quantum Einstein Gravity, showing its agreement with the established average action method and supporting the nonperturbative renormalizability hypothesis.

Findings

Confirmed the existence of a non-Gaussian fixed point.

Demonstrated perfect consistency between proper time and average action RG equations.

Validated the use of a special infrared regulator for precise critical exponents.

Abstract

We analyze a proper time renormalization group equation for Quantum Einstein Gravity in the Einstein-Hilbert truncation and compare its predictions to those of the conceptually different exact renormalization group equation of the effective average action. We employ a smooth infrared regulator of a special type which is known to give rise to extremely precise critical exponents in scalar theories. We find perfect consistency between the proper time and the average action renormalization group equations. In particular the proper time equation, too, predicts the existence of a non-Gaussian fixed point as it is necessary for the conjectured nonperturbative renormalizability of Quantum Einstein Gravity.