Trace Anomalies and Cocycles of Weyl and Diffeomorphisms Groups

Details Trace Anomalies and Cocycles of Weyl and Diffeomorphisms Groups Trace Anomalies and Cocycles of Weyl and Diffeomorphisms Groups

1994-11-08

arxiv.org/abs/hep-th/9411068v1

Mod.Phys.Lett.A11:409-422,1996

Physics

High Energy Physics

High Energy Physics - Theory

14 pages

Scientific paper

10.1142/S021773239600045X

The general structure of trace anomaly, suggested recently by Deser and Shwimmer, is argued to be the consequence of the Wess-Zumino consistency condition. The response of partition function on a finite Weyl transformation, which is connected with the cocycles of the Weyl group in $d=2k$ dimensions is considered, and explicit answers for $d=4,6$ are obtained. Particularly, it is shown, that addition of the special combination of the local counterterms leads to the simple form of that cocycle, quadratic over Weyl field $\sigma$, i.e. the form, similar to the two-dimensional Lioville action. This form also establishes the connection of the cocycles with conformal-invariant operators of order $d$ and zero weight. Beside that, the general rule for transformation of that cocycles into the cocycles of diffeomorphisms group is presented.

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