Einstein-Cartan gravity, Asymptotic Safety, and the running Immirzi parameter

TL;DR

This paper investigates the renormalization group flow of Einstein-Cartan gravity, exploring the potential for asymptotic safety and analyzing how the Immirzi parameter influences the theory's scale dependence.

Contribution

It develops a new methodology for analyzing the RG flow in Einstein-Cartan gravity and applies it to a three-dimensional truncated theory space including the Immirzi parameter.

Findings

Identifies a non-Gaussian fixed point suitable for asymptotic safety.

Analyzes the scale dependence of Newton's constant, cosmological constant, and Immirzi parameter.

Provides tools for future RG flow studies in Einstein-Cartan theories.

Abstract

In this paper we analyze the functional renormalization group flow of quantum gravity on the Einstein-Cartan theory space. The latter consists of all action functionals depending on the spin connection and the vielbein field (co-frame) which are invariant under both spacetime diffeomorphisms and local frame rotations. In the first part of the paper we develop a general methodology and corresponding calculational tools which can be used to analyze the flow equation for the pertinent effective average action for any truncation of this theory space. In the second part we apply it to a specific three-dimensional truncated theory space which is parametrized by Newton's constant, the cosmological constant, and the Immirzi parameter. A comprehensive analysis of their scale dependences is performed, and the possibility of defining an asymptotically safe theory on this hitherto unexplored theory space is investigated. In principle Asymptotic Safety of metric gravity (at least at the level of the effective average action) is neither necessary nor sufficient for Asymptotic Safety on the Einstein-Cartan theory space which might accommodate different "universality classes" of microscopic quantum gravity theories. Nevertheless, we do find evidence for the existence of at least one non-Gaussian renormalization group fixed point which seems suitable for the Asymptotic Safety construction in a setting where the spin connection and the vielbein are the fundamental field variables.