Grassmann-odd three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT

TL;DR

This paper analytically constructs three-point functions of conserved supercurrents in 3D $ ext{N}=1$ SCFT, proving the absence of parity-violating terms and the uniqueness of parity-even contributions across all superspins.

Contribution

It provides an explicit analytic proof that these correlators lack parity-violating parts and characterizes the parity-even sector for arbitrary superspins in 3D $ ext{N}=1$ superconformal theories.

Findings

No parity-violating contributions in these correlators.

Parity-even contributions are unique and exist for all superspins.

Explicit solutions for the parity-even sector are obtained for arbitrary superspins.

Abstract

We consider the analytic construction of three-point functions of conserved higher-spin supercurrents in three-dimensional $\mathcal{N}=1$ superconformal field theory which are Grassmann-odd in superspace. In particular, these include the three-point functions of the supercurrent and flavour currents, which contain the three-point functions of the energy-momentum tensor and conserved vector currents at the component level. We present an analytic proof for arbitrary superspins that these correlators do not possess a parity-violating contribution. We also prove that the parity-even contribution is unique, and exists (under an assumption that is well supported by the computational approach of arXiv:2302.00593) for arbitrary superspins. The construction of the parity-even sector is shown to reduce to solving a system of linear homogeneous equations with a tri-diagonal matrix of co-rank one, which we solve explicitly for arbitrary superspins.