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 $2\min (s_i)+1$.

arXiv comment40 pages. arXiv admin note: text overlap with arXiv:2210.13135

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Cited by in corpus (4)

• On correlation functions of higher-spin currents in arbitrary dimensions $d>3$
• Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins
• Superspace invariants and correlators in 4d $\mathcal{N}=1$ superconformal field theories
• Constructive approach to solution of the conservation condition for conformal higher spin tree-point correlation function with equal spins