Superconformal Symmetry and Correlation Functions

Four-dimensional N -extended superconformal symmetry and correlation functions of quasi-primary superfields are studied within the superspace formalism. A superconformal Killing equation is derived and its solutions are classified in terms of supertranslations, dilations, Lorentz transformations, R-symmetry transformations and special superconformal transformations. In general, due to the invariance under supertranslations and special superconformal transformations, superconformally invariant n-point functions reduce to one unspecified (n − 2)-point function which must transform homogeneously under the remaining rigid transformations, i.e. dilations, Lorentz transformations and R-symmetry transformations. Based on this result, we are able to identify all the superconformal invariants and obtain the general form of n-point functions for scalar superfields. In particular, as a byproduct, a selection rule for correlation functions of certain class of quasi-primary fields is derived, the existence of which in N = 4 super Yang-Mills theory was previously predicted in the context of AdS/CFT correspondence [1]. Superconformally covariant differential operators are also discussed. ∗E-mail address: [email protected]