Trace anomalies and cocycles of the Weyl group

The response of the partition function of six-dimensional classically Weyl-invariant theories on a finite Weyl transformation is calculated (this is a cocycle of the Weyl group, connected with the trace anomaly), and it is shown that this cocycle can be chosen quadratic over the Weyl field, in exact analogy with the two-dimensional Liouville action: S = ∫ d6x g (σΔ6σ+σ × Anomaly) where Δ6 is the zero weight conformal-invariant operator of order six, derived in the present letter. The structure of the trace anomaly as a direct consequence of the Wess-Zumino consistensy condition is discussed.