Cohomological structure of the conformal anomaly

A cohomological classification of conformal anomalies in the dimension $D=6$ is given. Different anomaly classes have a common origin from the cohomological standpoint, being equivalent to the Euler density $E_6$. The descent equation technique is developed for conformal anomalies by analogy with gauge theories. All highest cocycles of the Weyl group are investigated. The general technique for constructing all conformal anomalies from the Weyl density $E_{2n}$ in arbitrary space-time dimensions is presented. The principal difference between structures of these anomalies in dimensions $D=4$ and $D=6$ is demonstrated. A conformally invariant operator (constructed from Riemann and Ricci tensors, scalar curvature, and covariant derivatives) acting on a scalar with zero conformal weight is absent in $D=6$.