  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.
