Implications of N=1 superconformal symmetry for chiral fields

The requirements of N=1 superconformal invariance for the correlation functions of chiral superfields are analysed. Complete expressions are found for the three-point function for the general spin case and for the four-point function for scalar superfields for ∑qi=3 where qi is the scale dimension for the ith superfield and is related to the U(1) R-charge. In the latter case the relevant Ward identities reduce to eight differential equations for four functions of u,v which are invariants when the superconformal symmetry is reduced to the usual conformal group. The differential equations have a general solution given by four linearly independent expressions involving a two-variable generalisation of the hypergeometric function. By considering the behaviour under permutations, or crossing symmetry, the chiral four-point function is shown to be determined up to a single overall constant. The results are in accord with the supersymmetric operator product expansion.