Correlation Functions of Conserved Currents in Four Dimensional Conformal Field Theory

TL;DR

This paper derives a generating function for all 3-point functions of higher spin conserved currents in 4D conformal field theory, revealing a factorized form suggestive of free field realizations and exploring potential interacting theories.

Contribution

It provides a universal generating function for 3-point functions of higher spin currents and analyzes the possibility of interacting theories through 4-point functions.

Findings

3-point functions have a factorized form suggestive of free fields

A unique 4-point function candidate may correspond to an interacting theory

The 4-point function passes several consistency tests but its physical realization remains open

Abstract

We derive a generating function for all the 3-point functions of higher spin conserved currents in four dimensional conformal field theory. The resulting expressions have a rather surprising factorized form which suggest that they can all be realized by currents built from free massless fields of arbitrary (half-)integer spin s. This property is however not necessarily true also for the higher-point functions. As an illustration we analyze the general 4-point function of conserved abelian U(1) currents of scale dimension equal to three and find that apart from the two free field realizations there is a unique possible function which may correspond to an interacting theory. Although this function passes several non-trivial consistency tests, it remains an open challenging problem whether it can be actually realized in an interacting CFT.