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arXiv · 2106.14498

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

Evgeny I. Buchbinder·Jessica Hutomo·Sergei M. Kuzenko
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Abstract

In this paper, we study the general form of three-point functions of conserved current multiplets $S_{α(k)}= S_{(α_1 \dots α_k)}$ of arbitrary rank in four-dimensional ${\mathcal N}=1$ superconformal theory. We find that the correlation function of three such operators $\langle \bar{S}_{\dotα(k)} (z_1) S_{β(k+l)} (z_2) \bar{S}_{\dotγ(l)} (z_3) \rangle$ 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 $\langle \bar{S}_{\dotα(k)} (z_1) S_{α(k)} (z_2) L(z_3) \rangle$ and $\langle \bar{S}_{\dotα(k)} (z_1) S_{α(k)} (z_2) J_{γ\dotγ} (z_3) \rangle$, where $L$ is the flavour current multiplet and $J_{γ\dotγ}$ is the supercurrent.

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Evgeny I. Buchbinder, Jessica Hutomo, Sergei M. Kuzenko. 2021-07-13. Three-point functions of higher-spin spinor current multiplets in ${\mathcal N}=1$ superconformal theory. https://doi.org/10.1007/jhep10(2021)058

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