Superspace formulation and correlation functions of 3d superconformal field theories

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.