Local Anomalies, Local Equivariant Cohomology and the Variational Bicomplex

Abstract

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.

arXiv comment36 pages. The paper is divided in two parts

References in corpus (4)

• Local BRST cohomology in gauge theories
• General Solution of the Consistency Equation
• Equivariant characteristic classes in the bundle of connections
• Universal bundle for gravity, local index theorem, and covariant gravitational anomalies

Cited by in corpus (6)

• Conserved current for the Cotton tensor, black hole entropy and equivariant Pontryagin forms
• On the geometrical interpretation of locality in anomaly cancellation
• Differential characters and cohomology of the moduli of flat Connections
• Equivariant prequantization bundles on the space of connections and characteristic classes
• Equivariant holonomy of U(1)-bundles
• Pontryagin forms on $(4k-2)$-manifolds and symplectic structures on the spaces of Riemannian metrics