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

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.

Effective action from the functional renormalization group

“…We note that the intermediate results of the RG flow depend slightly on the choice of the cutoff kernel function R k (z). However, as discussed in [2,3,14,64], the evidences for existence of FPs (realizing the idea of asymptotic safety in the UV) are independent of this choice and the scheme of regularization and renormalization. The same is also true in the k → 0 limit of the EAA, while the interpolating effective action k at finite k > 0 shows a bit of dependence.…”