Conformal trace relations from the dilaton Wess–Zumino action

We use the method of Weyl-gauging in the determination of the Wess–Zumino conformal anomaly action to show that in any even (d=2k) 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 2k. 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