Three-point functions of conserved supercurrents in 3D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math> SCFT: General formalism for arbitrary superspins

We analyse the general structure of three-point functions conserved higher-spin supercurrents in 3D, $\mathcal{N}=1$ superconformal field theory. It is shown that supersymmetry imposes additional restrictions on correlation currents. develop a manifestly supersymmetric formalism to compute function $\langle \mathbf{J}^{}_{s_{1}} \mathbf{J}'_{s_{2}} \mathbf{J}''_{s_{3}} \rangle$, where $\mathbf{J}^{}_{s_{1}}$, $\mathbf{J}'_{s_{2}}$ and $\mathbf{J}''_{s_{3}}$ are with superspins $s_{1}$, $s_{2}$ $s_{3}$ respectively (integer or half-integer). Using computational approach limited only by computer power, we analytically impose constraints arising from superfield conservation equations symmetries under permutations superspace points. Explicit solutions for presented provide complete classification results $s_{i} \leq 20 $; pattern very clear, propose our holds arbitrary superspins. demonstrate Grassmann-even fixed up one parity-even parity-odd structure, while Grassmann-odd single structure. The existence subject set triangle inequalities For completeness, also involving scalar superfields.