Quantum Gravity, Torsion, Parity Violation and all that

TL;DR

This paper investigates parity violation in quantum gravity by analyzing fermion coupling with torsion and the Immirzi parameter, revealing conditions under which parity violation occurs and constraints on the parameter.

Contribution

It derives the low-energy effective Lagrangian in quantum gravity with torsion, clarifying the role of the Immirzi parameter and fermion coupling in parity violation.

Findings

Non-minimal coupling leads to parity violation via axial-vector interactions.

Real Immirzi parameter values are unconstrained by parity considerations.

Imaginary Immirzi parameter values cause unitarity violations and divergences.

Abstract

We discuss the issue of parity violation in quantum gravity. In particular, we study the coupling of fermionic degrees of freedom in the presence of torsion and the physical meaning of the Immirzi parameter from the viewpoint of effective field theory. We derive the low-energy effective lagrangian which turns out to involve two parameters, one measuring the non-minimal coupling of fermions in the presence of torsion, the other being the Immirzi parameter. In the case of non-minimal coupling the effective lagrangian contains an axial-vector interaction leading to parity violation. Alternatively, in the case of minimal coupling there is no parity violation and the effective lagrangian contains only the usual axial-axial interaction. In this situation the real values of the Immirzi parameter are not at all constrained. On the other hand, purely imaginary values of the Immirzi parameter lead to violations of unitarity for the case of non-minimal coupling. Finally, the effective lagrangian blows up for the positive and negative unit imaginary values of the Immirzi parameter.