We analyse the general structure of the three-point functions involving conserved higher-spin ``vector-like" supercurrents $J_{ s}(z) := J_{ \alpha(s) \dot{ \alpha}(s)}(z)$ in four-dimensional $\mathcal{ N}=1$ superconformal field theory. Using the constraints of superconformal symmetry and superfield conservation equations, we utilise a computational approach to analyse the general structure of the three-point function $\langle J^{ }_{ s_{ 1}}(z_{ 1}) \, J'_{ s_{ 2}}(z_{ 2}) \, J''_{ s_{ 3}}(z_{ 3}) \rangle$ and provide a general classification of the results. We demonstrate that the three-point function is fixed up to $2 \min (s_{ i}) + 2$ independent conserved structures, which we propose to hold for arbitrary superspins. In addition, we show that the conserved structures can be classified as parity-even or parity-odd in superspace based on their transformation properties under superinversion.
Categories: hep-th math-ph math.MP