The Immirzi parameter as an instanton angle

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.