Regulator dependence of fixed points in quantum Einstein gravity with $R^2$ truncation

TL;DR

This paper investigates how different regulator choices affect the fixed points in quantum Einstein gravity with an added $R^2$ term, identifying an optimal regulator that minimizes parameter dependence and analyzing fixed point stability.

Contribution

It introduces a functional renormalization group analysis including quadratic curvature terms and identifies the regulator that optimizes physical quantity stability.

Findings

The non-Gaussian fixed point is identified for various regulators.

The Litim regulator minimizes dependence of physical quantities on regulator choice.

The infrared fixed point's critical exponent is unaffected by the $R^2$ coupling.

Abstract

We performed a functional renormalization group analysis for the quantum Einstein gravity including a quadratic term in the curvature. The ultraviolet non-gaussian fixed point and its critical exponent for the correlation length are identified for different forms of regulators in case of dimension 3. We searched for that optimized regulator where the physical quantities show the least regulator parameter dependence. It is shown that the Litim regulator satisfies this condition. The infrared fixed point has also been investigated, it is found that the exponent is insensitive to the third coupling introduced by the $R^2$ term.