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

TL;DR

This paper develops a formalism to analyze three-point functions of conserved higher-spin currents in 3D CFTs, revealing they are generally fixed up to a few structures constrained by triangle inequalities.

Contribution

It introduces an automated computational approach to determine three-point functions involving arbitrary spins in 3D CFTs, including mixed correlators with scalars and spinors.

Findings

Three-point functions are fixed up to two even and one odd structure.

Correlation functions obey triangle inequalities.

The formalism applies to both bosonic and fermionic currents.

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 $\langle J^{}_{s_{1}} J'_{s_{2}} J''_{s_{3}} \rangle$, where $J^{}_{s_{1}}$, $J'_{s_{2}}$ and $J''_{s_{3}}$ 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.