Three-point functions of a superspin-2 current multiplet in 3D, N=1 superconformal theory

TL;DR

This paper computes three-point correlation functions of a superspin-2 current multiplet in 3D N=1 superconformal theories, revealing fixed structures in both parity-even and parity-odd sectors.

Contribution

It provides the first detailed calculation of three-point functions involving a superspin-2 current multiplet in 3D N=1 superconformal theories, including parity-odd contributions.

Findings

Parity-even and parity-odd sectors are each fixed up to one coefficient.

Presence of parity-odd structures is compatible with supersymmetry.

Correlation functions are constrained by conservation and permutation invariance.

Abstract

We consider $\mathcal{N=1}$ superconformal field theories in three-dimensions possessing a conserved current multiplet $\mathcal{F}_{ (\alpha_{1} \alpha_{2} \alpha_{3} \alpha_{4}) }$ which we refer to as the superspin-2 current multiplet. At the component level it contains a conserved spin-2 current different from the energy-momentum tensor and a conserved fermionic higher spin current of spin 5/2. Using a superspace formulation, we calculate correlation functions involving $\mathcal{F}$, focusing particularly on the three-point function $ \langle \mathcal{F} \mathcal{F} \mathcal{F} \rangle $. After imposing the constraints arising from conservation equations and invariance under permutation of superspace points, we find that the parity-even and parity-odd sectors of this three-point function are each fixed up to a single coefficient. The presence of the parity-odd contribution is rather non-trivial, as there is an apparent tension between supersymmetry and the existence of parity-odd structures.