  The possibility of parity violation in a gravitational theory with torsion is
extensively explored in four and higher dimensions. In the former case,we have
listed our conclusions on when and whether parity ceases to be conserved, with
both two-and three-index antisymmetry of the torsion field. In the latter, the
bulk spacetime is assumed to have torsion, and the survival of parity-violating
terms in the four dimensional effective action is studied, using the
compactification schemes proposed by Arkani-Hamed-Dimopoulos-Dvali and
Randall-Sundrum. An interesting conclusion is that the torsion-axion duality
arising in a stringy scenario via the second rank antisymmetric Kalb-Ramond
field leads to conservation of parity in the gravity sector in any dimension.
However, parity-violating interactions do appear for spin 1/2 fermions in such
theories, which can have crucial phenomenological implications.
