On selfdual spin-connections and Asymptotic Safety

TL;DR

This paper investigates Euclidean quantum gravity using selfdual or anti-selfdual spin-connections, establishing a new RG flow approach that suggests the theory may be asymptotically safe, similar to Einstein-Cartan gravity.

Contribution

It introduces a novel RG equation tailored for selfdual spin-connection variables and analyzes their non-perturbative renormalizability within a Holst action framework.

Findings

Selfdual theory likely asymptotically safe

RG flow indicates non-perturbative renormalizability

Comparable evidence to Einstein-Cartan gravity without selfduality

Abstract

We explore Euclidean quantum gravity using the tetrad field together with a selfdual or anti-selfdual spin-connection as the basic field variables. Setting up a functional renormalization group (RG) equation of a new type which is particularly suitable for the corresponding theory space we determine the non-perturbative RG flow within a two-parameter truncation suggested by the Holst action. We find that the (anti-)selfdual theory is likely to be asymptotically safe. The existing evidence for its non-perturbative renormalizability is comparable to that of Einstein-Cartan gravity without the selfduality condition.