On correlation functions of higher-spin currents in arbitrary dimensions $d>3$

TL;DR

This paper classifies and constructs conformal three-point functions of higher-spin currents in arbitrary dimensions, confirming their relation to higher-spin cubic vertices and setting the stage for a general solution in future work.

Contribution

It provides a complete solution for certain conserved higher-spin current correlators and links them to higher-spin cubic vertices, advancing the understanding of conformal higher-spin theories.

Findings

Confirmed the counting of independent structures matches higher-spin cubic vertices

Solved conservation conditions explicitly for some spins

Set up equations for general solutions to higher-spin correlators

Abstract

We revisit the problem of classification and explicit construction of the conformal three-point correlation functions of currents of arbitrary integer spin in arbitrary dimensions. For the conserved currents, we set up the equations for the conservation conditions and solve them completely for some values of spins, confirming the earlier counting of the number of independent structures matching them with the higher-spin cubic vertices in one higher dimension. The general solution for the correlators of conserved currents we delegate to a follow-up work.