Three-point functions of a superspin-2 current multiplet in 3D, N=1 superconformal theory

Abstract

We consider $\mathcal{N}=1$ superconformal field theories in three-dimensions possessing a conserved current multiplet ${\mathcal{F}}_{({\alpha }_1{\alpha }_2{\alpha }_3{\alpha }_4)}$ which we refer to as the superspin-2 current multiplet. At the component level it contains a conserved spin-2 current different from the energy-momentum tensor and a conserved fermionic higher spin current of spin 5/2. Using a superspace formulation, we calculate correlation functions involving $\mathcal{F}$, focusing particularly on the three-point function $⟨\mathcal{FFF}⟩$. After imposing the constraints arising from conservation equations and invariance under permutation of superspace points, we find that the parity-even and parity-odd sectors of this three-point function are each fixed up to a single coefficient. The presence of the parity-odd contribution is rather non-trivial, as there is an apparent tension between supersymmetry and the existence of parity-odd structures.

arXiv comment49 pages; v2: minor corrections, v3: minor corrections, published version

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• Superconformal invariants and spinning correlators in 3d $\mathcal{N}=2$ SCFTs
• 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
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• 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
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