The Immirzi Parameter as an Instanton Angle

TL;DR

This paper proposes a topological interpretation of the Barbero-Immirzi parameter in loop quantum gravity, linking it to a theta-term in Einstein-Cartan theory derived from de Sitter gauge symmetry breaking.

Contribution

It introduces a novel topological perspective on the Immirzi parameter by relating it to a theta-term in Einstein-Cartan gravity through gauge theory methods.

Findings

Immirzi parameter identified as a combination of fundamental constants and a theta-term.

Topological interpretation aligns with gauge theory principles.

Provides a new understanding of quantum gravity ambiguities.

Abstract

The Barbero-Immirzi parameter is a one parameter quantization ambiguity underpinning the loop approach to quantum gravity that bears tantalizing similarities to the theta parameter of gauge theories such as Yang-Mills and QCD. Despite the apparent semblance, the Barbero-Immirzi field has resisted a direct topological interpretation along the same lines as the theta-parameter. Here we offer such an interpretation. Our approach begins from the perspective of Einstein-Cartan gravity as the symmetry broken phase of a de Sitter gauge theory. From this angle, just as in ordinary gauge theories, a theta-term emerges from the requirement that the vacuum is stable against quantum mechanical tunneling. The Immirzi parameter is then identified as a combination of Newton's constant, the cosmological constant, and the theta-parameter.