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

Abstract

We analyse 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 analyse 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 vector-like 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 $2\min (s_i)+1$.

40 pages. arXiv admin note: text overlap with arXiv:2210.13135

References in corpus (2)

• Higher spin 3-point functions in 3d CFT using spinor-helicity variables
• Three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins

Cited by in corpus (1)

• Superspace invariants and correlators in 4d $\mathcal{N}=1$ superconformal field theories