Parity violation in metric-torsion theories of gravitation

Immirzi parameter, torsion, and discrete symmetries

“…However, it was pointed out recently in [2] (see also earlier paper [3]) that in the presence of spin 1/2 particles the second term in action (1) does not vanish on mass shell, and therefore γ should enter the corresponding equations of motion.…”

“…In connection with equation (7), the following question arises. The usual curvature tensor R IJ µν and its dual * R IJ µν behave in opposite ways both under the space reflection P and the time reversal T (see, e.g., [3]). To see it, we recall firstly that the duality transformation in electrodynamics results in E → B, B → −E, and that E and B behave in opposite ways both under P and T .…”

The spherically symmetric Standard Model with gravity

“…This action is linear in curvature. However, the term ε klmnR klmn is also linear in curvature and was considered in [68]. In case of vanishing torsion this term identically vanishes which was already mentioned in [69].…”

“…If torsion is present then the term gives additional contributions to the field equations. In [68] it was used to analyse parity violating contributions in the action. Fortunately it turns out that this term also vanishes identically if fermions are the source of torsion as in the SM under consideration.…”

Torsional instanton effects in quantum gravity

“…Thus, the electric dipole moment of neutron can develop a dependence on the Barbero-Immirzi parameter η (see ref. [2,34] for earlier discussions on parity violating effects in gravity).…”