Purely axial torsion pp-wave conjecture in quadratic metric-affine gravity

Consider quadratic metric-affine gravity with a pp-metric and explicitly given purely axial torsion whose Ricci curvature is parallel. Purely axial torsion pp-wave conjecture. There exists a class of spacetimes equipped with the pp-metric and explicitly given purely axial torsion of parallel Ricci curvature that satisfies the field equations. This is the proposed axial-torsion analogue of the generalised pp-waves obtained by combining a pp-metric with purely tensor torsion waves. The claim remains open in the source.