Mixed three-point functions of conserved currents in three-dimensional superconformal field theory

Abstract

We consider mixed three-point correlation functions of the supercurrent and flavour current in three-dimensional $1\le \mathcal{N}\le 4$ superconformal field theories. Our method is based on the decomposition of the relevant tensors into irreducible components to guarantee that all possible tensor structures are systematically taken into account. We show that only parity even structures appear in the correlation functions. In addition to the previous results obtained in arXiv:1503.04961, it follows that supersymmetry forbids parity odd structures in three-point functions involving the supercurrent and flavour current multiplets.

arXiv comment54 pages, v2: minor typos corrected, references added, v3: section 7 added, published version

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• Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ superconformal field theory
• Three-point functions of conserved currents in 3D CFT: general formalism for arbitrary spins
• Three-point functions of conserved currents in 4D CFT: general formalism for arbitrary spins
• Three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins
• Grassmann-odd three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT
• 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
• Three-point functions of higher-spin spinor current multiplets in $\mathcal{N}=1$ superconformal theory
• Three-point functions of fermionic higher-spin currents in 4D conformal field theory