Three‐Point Functions of Higher‐Spin Supercurrents in 4D N=1${{\cal N}}=1$ Superconformal Field Theory

We develop a general formalism to study the three-point correlation functions of conserved higher-spin supercurrent multiplets J α ( r ) ̇ $J_{\alpha (r) \dot{\alpha }(r)}$ in 4D N = 1 ${\cal N}=1$ superconformal theory. All constraints imposed by symmetry on function ⟨ β 2 γ 3 ⟩ $\langle J_{\alpha (r_1) }(r_1)} J_{\beta (r_2) \dot{\beta }(r_2) }J_{\gamma (r_3) \dot{\gamma }(r_3)}\rangle$ are systematically derived for arbitrary , $r_1, r_2, r_3$ thus reducing problem mostly computational and combinatorial. As an illustrative example, we explicitly work out allowed tensor structures contained }(r)} } J_{\gamma }}\rangle$ where }}$ is supercurrent. find that this depends two independent structures, though precise form correlator whether even or odd. The case $r=1$ reproduces ordinary Osborn. Additionally, present most structure mixed correlators L }(r)}\rangle$ }(r_2)} \rangle$ flavour current multiplet.