Renormalization Group Flow of the Holst Action

TL;DR

This paper investigates the renormalization group flow of quantum gravity using the Holst action with a focus on the Immirzi parameter, providing evidence for an asymptotically safe theory distinct from metric quantum gravity.

Contribution

It introduces a nonperturbative RG analysis of the Holst action with a running Immirzi parameter, suggesting a new asymptotically safe quantum gravity scenario.

Findings

Evidence for an asymptotically safe fixed point

Existence of a potentially inequivalent quantum gravity theory

Explicit solution of the RG equation in a three-parameter space

Abstract

The renormalization group (RG) properties of quantum gravity are explored, using the vielbein and the spin connection as the fundamental field variables. The scale dependent effective action is required to be invariant both under space time diffeomorphisms and local frame rotations. The nonperturbative RG equation is solved explicitly on the truncated theory space defined by a three parameter family of Holst-type actions which involve a running Immirzi parameter. We find evidence for the existence of an asymptotically safe fundamental theory, probably inequivalent to metric quantum gravity constructed in the same way.