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

Abstract

In this paper, we study the general form of three-point functions of conserved current multiplets $S_{\alpha(k)}= S_{(\alpha_1 \dots \alpha_k)}$ of arbitrary rank in four-dimensional ${\mathcal N}=1$ superconformal theory. We find that the correlation function of three such operators $\langle \bar{S}_{\dot{\alpha}(k)} (z_1) S_{\beta(k+l)} (z_2) \bar{S}_{\dot{\gamma}(l)} (z_3) \rangle$ 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 $\langle \bar{S}_{\dot{\alpha}(k)} (z_1) S_{\alpha(k)} (z_2) L(z_3) \rangle$ and $\langle \bar{S}_{\dot{\alpha}(k)} (z_1) S_{\alpha(k)} (z_2) J_{\gamma \dot{\gamma}} (z_3) \rangle$, where $L$ is the flavour current multiplet and $J_{\gamma \dot{\gamma}}$ is the supercurrent.