A geometrical description of local and global anomalies
A general topological scheme for testing the possible occurrence of anomalies in gauge theories in terms of the theory of group actions on line bundles was proposed in an earlier paper [cf.the authors, \textit{M. Martellini} and \textit{C. Reina}, Phys. Lett. B 172, No.2, 223-226 (1986)]. In the present letter this construction is modified in a manner that extends its range of application to a larger class of theories, allowing for a non-contractible configuration space and a non-connected gauge group. The underlying mathematical ingredient is the concept of a G-line bundle over a principal G-bundle p: \(P\to M\). (A line bundle L over P is a G-line bundle if there exists an action of the group G on L which is associative, fibre-preserving, and linear on the fibres.) In physical applications P is the configuration space and G is the invariance group of the theory. As an application of this theory the mechanisms of anomaly cancellation in gauge and string theories are briefly compared.
scientific article; zbMATH DE number 4133067