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

In this paper, we study the general form of three-point functions of conserved current multiplets Sα(k) = S(α1…αk) of arbitrary rank in four-dimensional $$ \mathcal{N} $$ N = 1 superconformal theory. We find that the correlation function of 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 ¯ α ̇ k z 1 S β k + l z 2 S ¯ γ ̇ l z 3 is fixed by the superconformal symmetry up to a single complex coefficient though the precise form of the correlator depends on the values of k and l. In addition, we present the general structure of mixed correlators of the form $$ \left\langle {\overline{S}}_{\dot{\alpha}(k)}\left({z}_1\right){S}_{\alpha (k)}\left({z}_2\right)L\left({z}_3\right)\right\rangle $$ S ¯ α ̇ k z 1 S α k z 2 L z 3 and $$ \left\langle {\overline{S}}_{\dot{\alpha}(k)}\left({z}_1\right){S}_{\alpha (k)}\left({z}_2\right){J}_{\gamma \dot{\gamma}}\left({z}_3\right)\right\rangle $$ S ¯ α ̇ k z 1 S α k z 2 J γ γ ̇ z 3 , where L is the flavour current multiplet and $$ {J}_{\gamma \dot{\gamma}} $$ J γ γ ̇ is the supercurrent.