Asymptotic safety and field parametrization dependence in the f(R) truncation

TL;DR

This paper investigates how the choice of field parametrization affects the fixed points and critical exponents in the $f(R)$ truncation of the functional renormalization group, revealing significant dependence beyond the Einstein-Hilbert level.

Contribution

It systematically analyzes the impact of field parametrization on fixed points and critical exponents in polynomial truncations within the $f(R)$ framework, highlighting qualitative differences.

Findings

Identification of two classes of fixed points with different relevant directions.

Demonstration of qualitative differences in results depending on parametrization.

Analysis of how regularization schemes influence fixed point structure.

Abstract

We study the dependence on field parametrization of the functional renormalization group equation in the $f(R)$ truncation for the effective average action. We perform a systematic analysis of the dependence of fixed points and critical exponents in polynomial truncations. We find that, beyond the Einstein-Hilbert truncation, results are qualitatively different depending on the choice of parametrization. In particular, we observe that there are two different classes of fixed points, one with three relevant directions and the other with two. The computations are performed in the background approximation. We compare our results with the available literature and analyze how different schemes in the regularizations can affect the fixed point structure.