Duality, generalized Chern–Simons terms and gauge transformations in a high dimensional curved spacetime

With two typical parent actions we have two kinds of dual worlds: (i) one of which contains an electric as well as magnetic current, and (ii) the other contains (generalized) Chern–Simons terms. All fields are defined on a curved spacetime of arbitrary (odd) dimensions. A new form of gauge transformations is introduced and plays an essential role in defining the interaction with a magnetic monopole or in defining the generalized Chern–Simons terms.