Renormalization group flows in area-metric gravity

TL;DR

This paper analyzes the renormalization group flows in area-metric gravity, a theory motivated by quantum gravity, showing how additional degrees of freedom decouple at low energies and exploring the behavior of key parameters.

Contribution

It provides the first analysis of RG flows in area-metric gravity, revealing how shape-mismatching degrees of freedom decouple and how the Immirzi parameter behaves under RG flow.

Findings

Masses tend to be large, ensuring decoupling of extra degrees of freedom.

Parity symmetry does not emerge under RG flow.

The Immirzi parameter's beta function has zeros at zero and infinite values.

Abstract

We put forward the first analysis of renormalization group flows in an area-metric theory, motivated by spin-foam quantum gravity. Area-metric gravity contains the well-known length-metric degrees of freedom of standard gravity as well as additional shape-mismatching degrees of freedom. To be phenomenologically viable, the shape-mismatching degrees of freedom have to decouple under the renormalization group flow towards lower scales. We test this scenario by calculating the renormalization group flow of the masses and find that these are in general even more relevant than dictated by their canonical scaling dimension. This generically results in masses which are large compared to the Planck mass and thereby ensure the decoupling of shape-mismatching degrees of freedom. In addition, the latter come in a left-handed and right-handed sector. We find that parity symmetry does not emerge under the renormalization group flow. Finally, we extract the renormalization group flow of the Immirzi parameter from this setup and find that its beta function features zeros at vanishing as well as at infinite Immirzi parameter.