N=1 superconformal symmetry in four dimensions

The N = 1, d = 4 superconformal group is studied and its representations are discussed. Under superconformal transformations, left invariant derivatives and some class of superfields, including supercurrents, are shown to follow these representations. In other words, these superfields are quasiprimary by analogy with two-dimensional conformal field theory. Based on these results, we find the general forms for the two-point and the three-point Green functions of the quasiprimary superfields in a group theoretical way. In particular, we prove that the two-point and the three-point Green functions of supercurrents are unique and present the explicit formulae of them.