For equal-spin currents up to spin four, conserved three-point correlators can be constructed explicitly as linear combinations of products of spin-one and spin-two Osborn-Petkou building blocks.
On correlation functions of higher-spin currents in arbitrary dimensions $d>3$
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abstract
We revisit the problem of classification and explicit construction of the conformal three-point correlation functions of currents of arbitrary integer spin in arbitrary dimensions. For the conserved currents, we set up the equations for the conservation conditions and solve them completely for some values of spins, confirming the earlier counting of the number of independent structures matching them with the higher-spin cubic vertices in one higher dimension. The general solution for the correlators of conserved currents we delegate to a follow-up work.
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Constructive approach to solution of the conservation condition for conformal higher spin tree-point correlation function with equal spins
For equal-spin currents up to spin four, conserved three-point correlators can be constructed explicitly as linear combinations of products of spin-one and spin-two Osborn-Petkou building blocks.