Local Anomalies, Local Equivariant Cohomology and the Variational Bicomplex

Details Local Anomalies, Local Equivariant Cohomology and the Variational Bicomplex Local Anomalies, Local Equivariant Cohomology and the Variational Bicomplex

2006-07-04

arxiv.org/abs/math-ph/0607005v2

Commun.Math.Phys.286:445-458,2009

Physics

Mathematical Physics

36 pages. The paper is divided in two parts

Scientific paper

10.1007/s00220-008-0703-2

The locality conditions for the vanishing of local anomalies in field theory are shown to admit a geometrical interpretation in terms of local equivariant cohomology, thus providing a method to deal with the problem of locality in the geometrical approaches to the study of local anomalies based on the Atiyah-Singer index theorem. The local cohomology is shown to be related to the cohomology of jet bundles by means of the variational bicomplex theory. Using these results and the techniques for the computation of the cohomology of invariant variational bicomplexes in terms of relative Gel'fand-Fuks cohomology introduced in [6], we obtain necessary and sufficient conditions for the cancellation of local gravitational and mixed anomalies.

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