Three-point functions of conserved currents in 3D CFT: general formalism for arbitrary spins

Abstract

We analyse the general structure of the three-point functions involving conserved bosonic and fermionic higher-spin currents in three-dimensional conformal field theory. Using the constraints of conformal symmetry and conservation equations, we use a computational formalism to analyse the general structure of $⟨J_{s_1}^{}{J}_{s_2}^{\prime }{J}_{s_3}^{\prime \prime }⟩$, where $J_{s_1}^{}$, $J_{s_2}^{\prime }$ and $J_{s_3}^{\prime \prime }$ are conserved currents with spins $s_1$, $s_2$ and $s_3$ respectively (integer or half-integer). The calculations are completely automated for any chosen spins and are limited only by computer power. We find that the correlation function is in general fixed up to two independent even structures, and one odd structure, subject to a set of triangle inequalities. We also analyse the structure of three-point functions involving higher-spin currents and fundamental scalars and spinors.

arXiv comment56 pages; v2: minor edits, references added

References in corpus (52)

• Correlation functions in the CFT(d)/AdS(d+1) correpondence
• Implications of Conformal Invariance in Field Theories for General Dimensions
• Spinning Conformal Correlators
• Chern-Simons Theory with Vector Fermion Matter
• Higher Spin Gauge Theory and Holography: The Three-Point Functions
• Conserved Currents and the Energy Momentum Tensor in Conformally Invariant Theories for General Dimensions
• Spinning Conformal Blocks
• Implications of conformal invariance in momentum space
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• A Natural Language for AdS/CFT Correlators
• 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
• Six-dimensional Methods for Four-dimensional Conformal Field Theories
• Correlation Functions of Conserved Currents in N = 2 Superconformal Theory
• N=1 Superconformal Symmetry in Four Dimensional Quantum Field Theory
• 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
• Renormalised 3-point functions of stress tensors and conserved currents in CFT
• Superconformal Symmetry and Correlation Functions
• Conformal correlators of mixed-symmetry tensors
• On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
• Supersymmetric Chern-Simons Theories with Vector Matter
• Constraining conformal field theories with a higher spin symmetry in d> 3 dimensions
• Lorentzian CFT 3-point functions in momentum space
• N=1 Superconformal Symmetry in Four 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
• Momentum space conformal three-point functions of conserved currents and a general spinning operator
• Exact Correlators from Conformal Ward Identities in Momentum Space and the Perturbative $TJJ$ Vertex
• Constraining conformal field theory with higher spin symmetry in four dimensions
• Superembedding methods for 4d N=1 SCFTs
• Higher spin 3-point functions in 3d CFT using spinor-helicity variables
• Chern-Simons Matter Theories and Higher Spin Gravity
• Momentum space parity-odd CFT 3-point functions
• A Complex Fermionic Tensor Model in $d$ Dimensions
• Superspace formulation and correlation functions of 3d superconformal field theories
• Momentum space spinning correlators and higher spin equations in three dimensions
• Relation between parity-even and parity-odd CFT correlation functions in three dimensions
• Superembedding Methods for Current Superfields
• Constraining momentum space correlators using slightly broken higher spin symmetry
• Six-dimensional Methods for Four-dimensional Conformal Field Theories II: Irreducible Fields
• 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
• Three-point functions of a superspin-2 current multiplet in 3D, N=1 superconformal theory
• Correlation functions in $\mathcal{N}=2$ Supersymmetric vector matter Chern-Simons 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

Cited by in corpus (6)

• 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
• On correlation functions of higher-spin currents in arbitrary dimensions $d>3$
• Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins
• Constructive approach to solution of the conservation condition for conformal higher spin tree-point correlation function with equal spins