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 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. © 2013 Elsevier B.V.