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.

56 pages; v2: minor edits, references added

References in corpus (4)

• Momentum space conformal three-point functions of conserved currents and a general spinning operator
• Higher spin 3-point functions in 3d CFT using spinor-helicity variables
• 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