Three-point functions of conserved currents in 4D CFT: General formalism for arbitrary spins

We analyze the general structure of the three-point functions involving conserved higher-spin currents $J_s≔J_{\alpha (i)\dot{\alpha }(j)}$ belonging to any Lorentz representation in four-dimensional conformal field theory. Using the constraints of conformal symmetry and conservation equations, we computationally analyze the general structure of three-point functions $⟨J_{s_1}{J}_{s_2}^{\prime }{J}_{s_3}^{\prime \prime }⟩$ for arbitrary spins and propose a classification of the results. For bosonic vectorlike currents with $i=j$, it is known that the number of independent conserved structures is $2\min (s_i)+1$. For the three-point functions of conserved currents with arbitrarily many dotted and undotted indices, we show that in many cases the number of structures deviates from $2\min (s_i)+1$.