Three-point functions of conserved currents in 3D CFT: General formalism for arbitrary spins

We analyze the general structure of the three-point functions involving conserved bosonic and fermionic higher-spin currents in three-dimensional conformal field theory. Using the constraints of conformal symmetry and conservation equations, we use a computational formalism to analyze the general structure of «Js1Js2′Js3′′», where Js1, Js2′, and Js3′′ are conserved currents with spins s1, s2, and s3 respectively (integer or half-integer). The calculations are completely automated for any chosen spins and are limited only by computer power. We find that the correlation function is in general fixed up to two independent "even"structures, and one "odd"structure, subject to a set of triangle inequalities. We also analyze the structure of three-point functions involving higher-spin currents and fundamental scalars and spinors. © 2023 authors.