The Immirzi Parameter as an Instanton Angle

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.

24 pages

References in corpus (6)

• Topological Interpretation of Barbero-Immirzi Parameter
• From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional
• Immirzi parameter and fermions with non-minimal coupling
• Superconducting loop quantum gravity and the cosmological constant
• Quantum gravity as a Fermi liquid
• Gravity from a fermionic condensate of a gauge theory