A possible topological interpretation of the Barbero-Immirzi parameter

TL;DR

This paper proposes a topological interpretation of the Barbero-Immirzi parameter by drawing an analogy with the theta-angle in Yang-Mills theories, linking it to the Nieh-Yan density and large gauge transformations.

Contribution

It introduces a novel topological perspective on the Barbero-Immirzi parameter, relating it to the Pontryagin class and large gauge sectors in torsional spacetimes.

Findings

Establishes a classical analogy between the Barbero-Immirzi parameter and the theta-angle.

Suggests the Barbero-Immirzi parameter as a free angular parameter in large gauge transformations.

Connects the large gauge sector with the Nieh-Yan density in quantum theory.

Abstract

A possible topological interpretation of the Barbero-Immirzi parameter is proposed. Classically, by generalizing the Holst action to torsional spacetimes, we construct a precise analogy between the Barbero--Immirzi parameter and the $\theta$-angle of Yang-Mills gauge theories, where the role of the Pontryagin class is played by a well known topological term containing the Holst modification, the Nieh--Yan density. Quantum mechanically, the same analogy requires to study the large gauge sector of the theory. In particular, it is argued that the large sector of the gauge group can be correlated with the Nieh-Yan density, while the Barbero-Immirzi parameter plays the role of the free angular parameter of the large gauge transformations.