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 (19)

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Cited by in corpus (10)

• Testing the role of the Barbero-Immirzi parameter and the choice of connection in Loop Quantum Gravity
• On the Role of Space-Time Foam in Breaking Supersymmetry via the Barbero-Immirzi Parameter
• Some cosmological models coming from gravitational theories having torsional degrees of freedom
• Gravity Asymptotics with Topological Parameters
• SU(2) gauge theory of gravity with topological invariants
• Modifications in the Spectrum of Primordial Gravitational Waves Induced by Instantonic Fluctuations
• Quantum-Ordering Ambiguities in Weak Chern-Simons 4D Gravity and Metastability of the Condensate-Induced Inflation
• Torsional instanton effects in quantum gravity
• Comments On Torsion and MacDowell-Mansouri gravity
• Barbero-Immirzi connections and how to build them