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All the constraints imposed by ${\\cal N}=1$ superconformal symmetry on the three-point function $\\langle J_{\\alpha(r_1) \\dot{\\alpha}(r_1)} J_{\\beta(r_2) \\dot{\\beta}(r_2) }J_{\\gamma(r_3) \\dot{\\gamma}(r_3)}\\rangle$ are systematically derived for arbitrary $r_1, r_2, r_3$, thus reducing the problem mostly to computational and combinatorial. 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Buchbinder, Gabriele Tartaglino-Mazzucchelli, Jessica Hutomo","submitted_at":"2022-08-15T08:09:22Z","abstract_excerpt":"We develop a general formalism to study the three-point correlation functions of conserved higher-spin supercurrent multiplets $J_{\\alpha(r) \\dot{\\alpha}(r)}$ in 4D ${\\cal N}=1$ superconformal theory. All the constraints imposed by ${\\cal N}=1$ superconformal symmetry on the three-point function $\\langle J_{\\alpha(r_1) \\dot{\\alpha}(r_1)} J_{\\beta(r_2) \\dot{\\beta}(r_2) }J_{\\gamma(r_3) \\dot{\\gamma}(r_3)}\\rangle$ are systematically derived for arbitrary $r_1, r_2, r_3$, thus reducing the problem mostly to computational and combinatorial. 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