A geometrical description of local and global anomalies
type: Item
instance of: scholarly article
title: A geometrical description of local and global anomalies
zbMATH Open document ID: 0692.53043
DOI: 10.1007/BF00402259
author: Roberto Catenacci
author: Gian Pietro Pirola
published in: Letters in Mathematical Physics
publication date: 1990-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 81T08
Mathematics Subject Classification ID: 81T30
zbMATH DE Number: 4133067
zbMATH Keywords: nonlinear \(\sigma\)-models
zbMATH Keywords: anomaly cancellation
zbMATH Keywords: anomalies
zbMATH Keywords: gauge theories
zbMATH Keywords: G-line bundle
zbMATH Keywords: string theories
reviewed by: Hanno Rund
MaRDI profile type: Publication
cites work: Dirac operators coupled to vector potentials
cites work: The aetiology of sigma model anomalies
cites work: BRS cohomology and topological anomalies
cites work: Algebraic geometry and the geometry of quantum strings
cites work: A note on the global structure of supermoduli spaces
cites work: Some remarks on the Gribov ambiguity
full work available at URL: https://doi.org/10.1007/bf00402259
OpenAlex ID: W2094482787
description: scientific article; zbMATH DE number 4133067