Mixed three-point functions of conserved currents in three-dimensional superconformal field theory

TL;DR

This paper analyzes mixed three-point functions of conserved currents in 3D superconformal field theories, revealing that only parity even structures are allowed due to supersymmetry constraints.

Contribution

It introduces a systematic tensor decomposition method to classify three-point functions, demonstrating that supersymmetry forbids parity odd structures in these correlators.

Findings

Only parity even structures appear in the correlation functions.

Supersymmetry constrains the tensor structures, forbidding parity odd terms.

The method extends previous classifications of superconformal correlators.

Abstract

We consider mixed three-point correlation functions of the supercurrent and flavour current in three-dimensional $1 \leq \mathcal{N} \leq 4$ superconformal field theories. Our method is based on the decomposition of the relevant tensors into irreducible components to guarantee that all possible tensor structures are systematically taken into account. We show that only parity even structures appear in the correlation functions. In addition to the previous results obtained in arXiv:1503.04961, it follows that supersymmetry forbids parity odd structures in three-point functions involving the supercurrent and flavour current multiplets.