Peccei--Quinn mechanism in gravity and the nature of the Barbero--Immirzi parameter

TL;DR

This paper explores the idea of treating the Barbero--Immirzi parameter as a dynamic field, linking it to quantum ambiguities via an analogy with the Peccei--Quinn mechanism in gravity.

Contribution

It introduces a novel perspective by promoting the Barbero--Immirzi parameter to a field and relates it to quantum ambiguities using a mechanism inspired by particle physics.

Findings

The Barbero--Immirzi parameter can be interpreted as a field rather than a constant.

A geometrical effective action is constructed to support this interpretation.

The analogy with the Peccei--Quinn mechanism provides a new way to understand quantum ambiguities.

Abstract

A general argument provides the motivation to consider the Barbero--Immirzi parameter as a field. The specific form of the geometrical effective action allows to relate the value of the Barbero--Immirzi parameter to other quantum ambiguities through the analog of the Peccei--Quinn mechanism.