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

TL;DR

This paper develops a method to construct and analyze 3-point correlators of spinning operators in 4d $ ext{N}=1$ superconformal field theories using superspace and polarization spinor techniques, providing new structural insights.

Contribution

It introduces a systematic construction of superspace invariants for 3-point correlators in 4d $ ext{N}=1$ SCFTs, extending non-supersymmetric results and applying them to conserved supercurrents.

Findings

Constructed 3-point superconformal invariants using polarization spinors.

Enumerated the form of spinning 3-point correlators in $ ext{N}=1$ SCFTs.

Derived additional constraints for correlators involving conserved supercurrents.

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.