Topologically modified teleparallelism, passing through the Nieh-Yan functional

Recently, generalizations of the Ashtekar constraints are derived via the Nieh-Yan topological term. To be fair, such canonical transformations have been applied before in a gauge framework of gravity. Moreover, in the case of the teleparallelism equivalent of Einstein’s theory, one can go further and show that the Chern-Simons solutions of the Gauss-type constraints wind around torsional instantons, thus establishing an analogue to the $\theta$ vacua of Yang-Mills theory.