Implications of N=4 superconformal symmetry in three spacetime dimensions

Abstract

We study implications of N=4 superconformal symmetry in three dimensions, thus extending our earlier results in arXiv:1503.04961 devoted to the N=1,2,3 cases. We show that the three-point function of the supercurrent in N=4 superconformal field theories contains two linearly independent forms. However, only one of these structures contributes to the three-point function of the energy-momentum tensor and the other one is present in those N=4 superconformal theories which are not invariant under the mirror map. We point out that general N=4 superconformal field theories admit two inequivalent flavour current multiplets and show that the three-point function of each of them is determined by one tensor structure. As an example, we compute the two- and three-point functions of the conserved currents in N=4 superconformal models of free hypermultiplets. We also derive the universal relations between the coefficients appearing in the two- and three-point correlators of the supercurrent and flavour current multiplets in all superconformal theories with N=1,2,3,4 supersymmetry. Our derivation is based on the use of Ward identities in conjunction with superspace reduction techniques.

75 pages

References in corpus (5)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Algebraic structures on parallel M2-branes
• Fractional M2-branes
• Off-shell superconformal nonlinear sigma-models in three dimensions
• Three-dimensional N=4 supersymmetry in harmonic N=3 superspace

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• Correlation functions of spinor current multiplets in $\mathcal{N}=1$ superconformal theory
• 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
• On superconformal Chern-Simons-matter theories in N=4 superspace
• 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
• Three-point functions of fermionic higher-spin currents in 4D conformal field theory
• Three-point functions of higher-spin spinor current multiplets in $\mathcal{N}=1$ superconformal theory