Grassmann-odd three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT

Abstract

We consider the analytic construction of three-point functions of conserved higher-spin supercurrents in three-dimensional $\mathcal{N}=1$ superconformal field theory which are Grassmann-odd in superspace. In particular, these include the three-point functions of the supercurrent and flavour currents, which contain the three-point functions of the energy-momentum tensor and conserved vector currents at the component level. We present an analytic proof for arbitrary superspins that these correlators do not possess a parity-violating contribution. We also prove that the parity-even contribution is unique, and exists (under an assumption that is well supported by the computational approach of arXiv:2302.00593) for arbitrary superspins. The construction of the parity-even sector is shown to reduce to solving a system of linear homogeneous equations with a tri-diagonal matrix of co-rank one, which we solve explicitly for arbitrary superspins.

arXiv comment33 pages

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Cited by in corpus (3)

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