N=1 Superconformal Symmetry in Four Dimensional Quantum Field Theory

The implications of N=1 superconformal symmetry for four dimensional quantum field theories are studied. Superconformal covariant expressions for two and three point functions of quasi-primary superfields of arbitrary spin are found and connected with the operator product expansion. The general formulae are specialised to cases involving a scalar superfield L, which contains global symmetry currents, and the supercurrent, which contains the energy momentum tensor, and the consequences of superconformal Ward identities analysed. The three point function of L is shown to have unique completely antisymmetric or symmetric forms. In the latter case the superspace version of the axial anomaly equation is obtained. The three point function for the supercurrent is shown to have two linearly independent forms. A linear combination of the associated coefficients for the general expression is shown to be related to the scale of the supercurrent two point function through Ward identities. The coefficients are given for the two free field superconformal theories and are also connected with the parameters present in the supercurrent anomaly for supergravity backgrounds. Superconformal invariants, which are possible even in three point functions, are discussed.