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.