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.
Highlights
The well-known fact that quantum gravity based on the Einstein-Hilbert theory is not perturbatively renormalizable [1–3] has motivated the construction of different approaches to quantum gravity beyond the standard quantum field theory realm
We study the dependence on field parametrization of the functional renormalization group equation in the fðRÞ truncation for the effective average action
In addition to the fðRÞ truncation, we made use of the so-called background approximation, which consists in expanding the effective average action up to second order in the fluctuation hμν
Summary
The well-known fact that quantum gravity based on the Einstein-Hilbert theory is not perturbatively renormalizable [1–3] has motivated the construction of different approaches to quantum gravity beyond the standard quantum field theory realm. The asymptotic safety program for the quantization of the gravitational interaction, which was introduced by Weinberg in [20], is a possible candidate of the formulation for quantum gravity as a continuum quantum field theory; see review papers [21–25] and the recent [26] It is crucial for the asymptotic safety scenario that the theory has a nontrivial fixed point in the renormalization group (RG) flow, a property which ensures the “nonperturbative” renormalizability of the theory. The coupling constants of the operators corresponding to the relevant directions become free parameters to be fixed by experiments In this way, asymptotically safe quantum gravity could lead to an ultraviolet (UV) complete theory. We investigate how different choices of field parametrization affect the fixed point analysis in fðRÞ truncations for the effective average action.
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