Superspace formulation and correlation functions of 3d superconformal field theories

TL;DR

This paper develops a superspace formalism for 3d superconformal field theories, classifies superfields and higher spin current multiplets, and constructs superconformal invariants for 3-point functions across various supersymmetries.

Contribution

It introduces a systematic superspace approach for 3d SCFTs, identifying invariants and relations for higher spin correlators, advancing the understanding of superconformal structures.

Findings

Classified superfields and higher spin multiplets in free 3d SCFTs.

Constructed superconformal invariants for 3-point functions.

Derived relations between invariants and explicit structures for various supersymmetries.

Abstract

We study $3d$ SCFTs in the superspace formalism and discuss superfields and on-shell higher spin current multiplets in free $3d$ SCFTs with $\mathcal{N}= 1,2,3,4$ and $6$ superconformal symmetry. For $\mathcal{N}=1$ 3d SCFTs we determine the superconformal invariants in superspace needed for constructing 3-point functions of higher spin operators, find the non-linear relations between the invariants and consequently write down all the independent invariant structures, both parity even and odd, for various 3-point functions of higher spin operators.