We establish a correspondence between superembedding and supertwistor methods for constructing 4D N = 1 SCFT correlation functions by deriving a simple relation between tensors used in the two methods. Our discussion applies equally to 4D CFTs by simply reducing all formulas to the N = 0 case.
We extend the superembedding formalism for 4D N=1 superconformal field theory (SCFT) to the case of fields in arbitrary representations of the superconformal group SU(2,2|1). As applications we obtain manifestly superconformally covariant expressions
for two- and three-point functions involving conserved currents, e.g. the supercurrent multiplet or global symmetry current superfields. The embedding space results are presented in a compact form by employing an index-free formalism. Our expressions are consistent with the literature, but the manifestly covariant forms of correlators presented here are new.
