Superspace invariants and correlators in 4d $\mathcal{N}=1$ superconformal field theories

Abstract

Using polarization spinor methods in conjunction with the superspace formalism, we construct 3-point superconformal invariants that are used to determine the form of 3-point correlators of spinning superfield operators in $\mathcal{N}=1$ superconformal field theories (SCFTs) in 4-dimensions. We enumerate the structural form of various spinning 3-point correlators using these invariants and find additional constraints on their form when the operators are conserved supercurrents. For these purposes, we first construct the invariants and 3-point correlators in non-supersymmetric $4d$ CFTs which are then extended using superspace methods to $4d$ SCFTs.