Abelian tensor hierarchy in 4D, N = 1 superspace

With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by kaluza-klein compactification from type ii theory or m-theory in a closed form, we embed the (abelian) tensor hierarchy of p-forms in four-dimensional, n =1superspaceandconstructitschern-simons-likeinvariants. whenspecializedtothe case in which the tensors arise from a higher-dimensional theory, the invariants be interpreted as higher-dimensional chern-simons forms reduced to four dimensions. as an application of the formalism, we construct the eleven-dimensional chern-simons form in terms of four-dimensional, n = 1 superfields.