TRACE ANOMALIES AND COCYCLES OF WEYL AND DIFFEOMORPHISMS GROUPS

The general structure of trace anomaly, suggested recently by Deser an d Schwimmer is argued to be the consequence of the Wess-Zumino consist ency condition. The response of partition function on a finite Weyl tr ansformation, which is connected with the cocycles of the Weyl group i n d = 2k dimensions is considered, and explicit answers for d = 4, 6 a re obtained. In particular, it is shown that addition of the special c ombination of the local counterterms leads to the simple form of that cocycle, quadratic over Weyl field sigma, i.e. the form, similar to th e two-dimensional Liouville action. This form also establishes the con nection of the cocycles with conformal-invariant operators of order d and zero weight. We also give the general rule for transformation of t hat cocycles into the cocycles of diffeomorphisms group.