Three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins

Abstract

We analyse the general structure of the three-point functions of conserved higher-spin supercurrents in 3D, $\mathcal{N}=1$ superconformal field theory. It is shown that supersymmetry imposes additional restrictions on correlation functions of conserved higher-spin currents. We develop a manifestly supersymmetric formalism to compute the three-point function $⟨{\mathbf{J}}_{s_1}^{}{\mathbf{J}}_{s_2}^{\prime }{\mathbf{J}}_{s_3}^{\prime \prime }⟩$, where ${\mathbf{J}}_{s_1}^{}$, ${\mathbf{J}}_{s_2}^{\prime }$ and ${\mathbf{J}}_{s_3}^{\prime \prime }$ are conserved higher-spin supercurrents with superspins $s_1$, $s_2$ and $s_3$ respectively (integer or half-integer). Using a computational approach limited only by computer power, we analytically impose the constraints arising from the superfield conservation equations and symmetries under permutations of superspace points. Explicit solutions for three-point functions are presented and we provide a complete classification of the results for $s_i\le 20$; the pattern is very clear, and we propose that our classification holds for arbitrary superspins. We demonstrate that Grassmann-even three-point functions are fixed up to one parity-even structure and one parity-odd structure, while Grassmann-odd three-point functions are fixed up to a single parity-even structure. The existence of the parity-odd structure in the Grassmann-even correlation functions is subject to a set of triangle inequalities in the superspins. For completeness, we also analyse the structure of three-point functions involving conserved higher-spin supercurrents and scalar superfields.

arXiv comment54 pages; v2: minor corrections, references added. arXiv admin note: substantial text overlap with arXiv:2210.13135

References in corpus (37)

• Implications of Conformal Invariance in Field Theories for General Dimensions
• Spinning Conformal Correlators
• Chern-Simons Theory with Vector Fermion Matter
• Conserved Currents and the Energy Momentum Tensor in Conformally Invariant Theories for General Dimensions
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• Constraining conformal field theories with a slightly broken higher spin symmetry
• Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Correlation Functions of Conserved Currents in N = 2 Superconformal Theory
• N=1 Superconformal Symmetry in Four Dimensional Quantum Field Theory
• On the uniqueness of higher-spin symmetries in AdS and CFT
• Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory
• Correlators of Large N Fermionic Chern-Simons Vector Models
• Light-Front Bootstrap for Chern-Simons Matter Theories
• Superconformal Symmetry and Correlation Functions
• On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
• Supersymmetric Chern-Simons Theories with Vector Matter
• On compactified harmonic/projective superspace, 5D superconformal theories, and all that
• Constraining conformal field theories with a higher spin symmetry in d> 3 dimensions
• Superconformal Symmetry in Three-dimensions
• Superconformal Symmetry in Six-dimensions and Its Reduction to Four
• General Three-Point Functions in 4D CFT
• Correlation Functions of Conserved Currents in Four Dimensional Conformal Field Theory
• Exact higher-spin symmetry in CFT: free fermion correlators from Vasiliev Theory
• Off-shell superconformal nonlinear sigma-models in three dimensions
• Constraining conformal field theory with higher spin symmetry in four dimensions
• Chern-Simons Matter Theories and Higher Spin Gravity
• Superspace formulation and correlation functions of 3d superconformal field theories
• Lectures on nonlinear sigma-models in projective superspace
• Implications of N=4 superconformal symmetry in three spacetime dimensions
• Mixed three-point functions of conserved currents in three-dimensional superconformal field theory
• Implications of N=5, 6 superconformal symmetry in three spacetime dimensions
• Correlation functions in $\mathcal{N}=2$ Supersymmetric vector matter Chern-Simons theory
• Three-point functions of a superspin-2 current multiplet in 3D, N=1 superconformal theory
• 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

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• Superspace invariants and correlators in 4d $\mathcal{N}=1$ superconformal field theories