A note on three-point functions of conserved currents

TL;DR

This paper derives the general form of three-point functions of conserved currents in conformal field theories across various dimensions, revealing new structures especially in odd dimensions.

Contribution

It provides a comprehensive classification of three-point functions of conserved currents in arbitrary dimensions, including new structures in odd dimensions not generated by known CFTs.

Findings

Explicit form of three-point functions fixed by symmetry and conservation

Generating functionals for all structures in any dimension

Identification of new structures in odd dimensions d>3

Abstract

We find the form of three-point correlation functions of traceless symmetric conserved currents of arbitrary spin in d-dimensional conformal field theory (CFT). These are fixed up to several constants by conformal symmetry and current conservation conditions. We present generating functionals for all structures in arbitrary d. In even dimensions we present an interpretation for each structure in terms of the corresponding free field. In odd dimensions d>3 an infinite number of structures is found which are not generated by known CFTs.