Parity violation in metric-torsion theories of gravitation

The general structure of metric-torsion theories of gravitation is shown to allow a parity-violating contribution to the complete action which is linear in the curvature tensor and vanishes identically in the absence of torsion. The resulting action involves apart from the Newtonian constant a coupling which governs the strength of the predicted parity-nonconserving ''interactions'' mediated by torsion. We consider this theory in the presence of the Proca field and show that it leads to a parity-violating term in the field equations in contrast to the Einstein-Cartan-Sciama-Kibble theory, which we use as a particularly simple example of a metric-torsion theory of gravitation.