Gauge theory of gravity with topological invariants

Abstract

In gravity theory in four dimensions, there are three possible topological terms which can be added to the Lagrangian density. These are the Nieh Yan, Pontryagin and Euler terms. Here we investigate the e_ect of these terms in the context of canonical SU(2) formulation of gravity. We set up a general SU(2) formulation for gravity including all three terms. The theory contains three topological parameters associated with the three terms. Finally, we study what could be a suitable quantum framework for gravity in which one of these parameters, namely the Barbero-Immirzi parameter, can be interpreted as a vacuum angle exactly like the theta parameter in gauge theories.