Generalizations of the Nieh-Yan topological invariant

We report new topological invariants in four dimensions that are generalizations of the Nieh-Yan topological invariant. The new topological invariants are obtained through a systematic method along the lines of the one used to get the Nieh-Yan form, but involving an SO(4,1) [SO(5)] connection constructed out from an SO(3,1) [SO(4)] connection and three SO(3,1) [SO(4)] tensor 1-forms. We give explicit expressions of the new 4-forms that give rise to the new topological invariants for particular choices of these 1-forms and show that the Nieh-Yan form arises as a particular case.