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 $⟨{\bar{S}}_{\dot{\alpha }(k)}(z_1)S_{\beta (k+l)}(z_2){\bar{S}}_{\dot{\gamma }(l)}(z_3)⟩$ 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 $⟨{\bar{S}}_{\dot{\alpha }(k)}(z_1)S_{\alpha (k)}(z_2)L(z_3)⟩$ and $⟨{\bar{S}}_{\dot{\alpha }(k)}(z_1)S_{\alpha (k)}(z_2)J_{\gamma \dot{\gamma }}(z_3)⟩$, where $L$ is the flavour current multiplet and $J_{\gamma \dot{\gamma }}$ is the supercurrent.

arXiv comment33 pages; V2: comments and references added

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