The aetiology of sigma model anomalies
type: Item
instance of: scholarly article
title: The aetiology of sigma model anomalies
zbMATH Open document ID: 0594.58046
DOI: 10.1007/BF01212688
published in: Communications in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: Certain nonlinear sigma models with fermions are ill-defined due to an anomaly which exhibits characteristics of both the nonabelian gauge theory anomaly and the SU(2) anomaly. The simplest way to diagnose the anomaly involves consideration of the global topology of the theory. In this paper, the authors review the mathematical methods needed for this analysis and apply them to several supersymmetric sigma models. Some of these are found to be anomalous. This paper includes eight sections and four appendices. In Section 2, the authors characterize the anomaly as an obstruction to a continuous definition of the functional on the map space \({\mathcal C}\). The condition obtained is that an integer \(\nu\) should vanish. A physical interpretation to this obstruction is given in Section 3. It is shown that for \(\nu\) \(\neq 0\) it is impossible to find well-behaved local counterterms which render different perturbative expansions of the same Green function physically equivalent. In Section 4, the authors compute \(\nu\), arriving at the final anomaly criterion which essentially says that (\({\mathcal F})^ 3\), \({\mathcal F}\) being the curvature or ''field strength'', should be an exact 6-form. Here and in the appendices, brief and useful descriptions of the needed mathematical tools can be found. Sections 5-7 are devoted to the applications of the anomaly criterion to some models.
Mathematics Subject Classification ID: 37N99
Mathematics Subject Classification ID: 81T08
zbMATH DE Number: 3956061
zbMATH Keywords: anomaly
zbMATH Keywords: SU(2) anomaly
zbMATH Keywords: supersymmetric sigma models
author: G. W. Moore
author: P. A. Nelson
reviewed by: Yanglian Pan
MaRDI profile type: Publication
cites work: Q3726964
cites work: Dirac operators coupled to vector potentials
cites work: Gravitational anomalies and the family's index theorem
cites work: The structure of gauge and gravitational anomalies
cites work: Anomalies and odd dimensions
cites work: Some remarks on BRS transformations, anomalies and the cohomology of the Lie algebra of the group of gauge transformations
cites work: Some remarks on the Gribov ambiguity
cites work: Q3961493
cites work: Q3874497
cites work: Q5545278
cites work: Q5607109
cites work: Q5825483
cites work: The index of elliptic operators. IV, V
cites work: On stochasticity in the von Foerster hyperbolic partial differential equation system. Further applications to the modeling of an asynchronously dividing cellular system
cites work: Q3734212
cites work: Q4073488
cites work: Supersymmetry and the Atiyah-Singer index theorem
cites work: FREDHOLM COMPLEXES
cites work: BOTT PERIODICITY AND THE INDEX OF ELLIPTIC OPERATORS
cites work: The index of elliptic operators. III
cites work: Q5572926
cites work: Q5601274
cites work: Complex manifolds without potential theory. (With an appendix on the geometry of characteristic classes). 2nd ed
cites work: Characteristic Classes. (AM-76)
cites work: Effective action for composite operators
cites work: Q3897665
cites work: Clifford modules
cites work: Q5521308
cites work: Some remarks on the paper of Callias
cites work: Q4765335
full work available at URL: https://doi.org/10.1007/bf01212688
OpenAlex ID: W1975579783
description: scientific article; zbMATH DE number 3956061