Correlation functions of spinor current multiplets in $\mathcal{N}=1$ superconformal theory

Abstract

We consider $\mathcal{N}=1$ superconformal field theories in four dimensions possessing an additional conserved spinor current multiplet $S_{\alpha }$ and study three-point functions involving such an operator. A conserved spinor current multiplet naturally exists in superconformal theories with $\mathcal{N}=2$ supersymmetry and contains the current of the second supersymmetry. However, we do not assume $\mathcal{N}=2$ supersymmetry. We show that the three-point function of two spinor current multiplets and the $\mathcal{N}=1$ supercurrent depends on three independent tensor structures and, in general, is not contained in the three-point function of the $\mathcal{N}=2$ supercurrent. It then follows, based on symmetry considerations only, that the existence of one more Grassmann odd current multiplet in $\mathcal{N}=1$ superconformal field theory does not necessarily imply $\mathcal{N}=2$ superconformal symmetry.

arXiv comment41 pages; V2: Typos corrected, published version; V3: minor corrections

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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 supercurrents in 3D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins
• Three-point functions of conserved currents in 4D CFT: general formalism for arbitrary spins
• 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
• 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
• Superspace invariants and correlators in 4d $\mathcal{N}=1$ superconformal field theories