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.
Highlights
It has recently been realized that non-abelian Chern-Simons theories coupled to fundamental matter fields in 3 dimensions are exactly solvable in the large N limit
We study 3d SCFTs in the superspace formalism and discuss superfields and on-shell higher spin current multiplets in free 3d SCFTs with N = 1, 2, 3, 4 and 6 superconformal symmetry
It should be possible to extend the results of Maldacena and Zhiboedov [3, 4] to obtain the exact form of the higher spin current algebra and the correlation functions of supersymmetric Chern-Simons coupled to fundamental matter fields with minimal matter content
Summary
It has recently been realized that non-abelian Chern-Simons theories coupled to fundamental matter fields in 3 dimensions are exactly solvable in the large N limit. It should be possible to extend the results of Maldacena and Zhiboedov [3, 4] to obtain the exact form of the higher spin current algebra and the correlation functions of supersymmetric Chern-Simons coupled to fundamental matter fields with minimal matter content. In order to extend recent results in the study of matter Chern-Simons theories to their supersymmetric counterparts, it would be convenient to have a formulation of these theories in superspace.
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