Wave Function Renormalization in Asymptotically Safe Quantum Gravity

TL;DR

This paper investigates wave function renormalization effects in asymptotically safe quantum gravity, identifying invariant quantities and analyzing the renormalization group flow of key parameters like Newton's constant and vacuum energy.

Contribution

It introduces WFR-invariant quantities and reformulates RG equations in terms of these, providing new insights into the flow of fundamental gravitational parameters.

Findings

Identification of two WFR-invariant quantities

RG equations can be expressed using these invariants

Behavior of vacuum energy near the low-energy singular barrier

Abstract

We discuss the effect of wave function renormalization (WFR) in asymptotically safe gravity. We show that there are two WFR-invariant quantities, and the renormalization (RG) equations may be written entirely in terms of these quantities. The same set of RG equations can be obtained whether we fix the vacuum energy or Newton coupling along the RG trajectory. The flow of the Newton constant and the vacuum energy is also discussed in detail. In particular we discuss how the vacuum energy behaves near the singular barrier in the low energy.