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

TL;DR

This paper derives the general form of three-point functions involving higher-spin conserved current multiplets in 4D ${ m N}=1$ superconformal theory, showing they are fixed by symmetry up to a single coefficient.

Contribution

It provides the explicit structure of three-point correlators of higher-spin multiplets and mixed correlators with flavor and supercurrent multiplets, extending superconformal symmetry constraints.

Findings

Three-point functions are fixed by superconformal symmetry up to one coefficient.

Explicit form of correlators depends on the ranks of the multiplets.

Mixed correlators with flavor and supercurrent multiplets are characterized.

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.