Conformal Trace Relations from the Dilaton Wess-Zumino Action

TL;DR

This paper demonstrates that in even-dimensional conformal field theories, all trace correlation functions can be derived from a finite set of lower-order correlators using the Wess-Zumino action and Weyl-gauging techniques.

Contribution

It explicitly derives the hierarchy of trace correlators in even dimensions, showing that only a limited set of correlators are independent, with the rest generated recursively.

Findings

In 4D, only the first 4 traced correlators are independent.

Higher-order correlators are recursively generated from lower-order ones.

The hierarchy is governed by the cocycle condition of the Wess-Zumino action.

Abstract

We use the method of Weyl-gauging in the determination of the Wess-Zumino conformal anomaly action, to show that in any even ($d = 2 k$) dimensions all the hierarchy of correlation functions involving traces of the energy-momentum tensor is determined in terms of those of lower orders, up to $2 k$. We work out explicitly the case $d=4$, and show that in this case in any conformal field theory only the first 4 traced correlators are independent. All the remaining correlators are recursively generated by the first 4. The result is a consequence of the cocycle condition which defines the Wess-Zumino action and of the finite order of its dilaton interactions.