Three-point functions of higher-spin spinor current multiplets in $$ \mathcal{N} $$ = 1 superconformal theory

A bstract In this paper, we study the general form of three-point functions conserved current multiplets S ? ( k ) = 1… ?k arbitrary rank in four-dimensional $$ \mathcal{N} N 1 superconformal theory. We find that correlation function three such operators \left\langle {\overline{S}}_{\dot{\alpha}(k)}\left({z}_1\right){S}_{\beta \left(k+l\right)}\left({z}_2\right){\overline{S}}_{\dot{\gamma}(l)}\left({z}_3\right)\right\rangle S ¯ ? ? k z 1 ? + l 2 ? 3 is fixed by symmetry up to a single complex coefficient though precise correlator depends on values and l . addition, present structure mixed correlators {\overline{S}}_{\dot{\alpha}(k)}\left({z}_1\right){S}_{\alpha (k)}\left({z}_2\right)L\left({z}_3\right)\right\rangle L (k)}\left({z}_2\right){J}_{\gamma \dot{\gamma}}\left({z}_3\right)\right\rangle J , where L flavour multiplet {J}_{\gamma \dot{\gamma}} supercurrent.