The evaluation map in field theory, sigma-models and strings. II
type: Item
instance of: scholarly article
title: The evaluation map in field theory, sigma-models and strings. II
zbMATH Open document ID: 0655.53069
DOI: 10.1007/BF01242137
published in: Communications in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: This paper presents a systematic analysis of local anomalies in sigma- models and strings and of global anomalies for both sigma-models and field theories. As in part I of the series [ibid. 112, 237-282 (1987; Zbl 0645.53071)], which dealt with local anomalies in field theories, the basic tool is a certain evaluation map, in this case \(ev: M\times Map(M,T)\to T,\) where M is a compact connected oriented n-dimensional Riemannian manifold (``space-time''), T the target space (connected Riemannian) of the sigma-model and Map(M,T) the space of \(C^{\infty}\)- maps from M to T. The authors point out a certain parallelism of \(\sigma\)-models with field theories, where T is replaced by the universal classifying space of the relevant principal fibre bundle. There is an important difference, however, as a generalized Wess-Zumino term may cancel an anomaly. In the case of strings both field-theory anomalies (gravitational and conformal, the latter being interpreted as a special case of holomorphic anomalies) and sigma-model anomalies are considered and the conditions on the background manifold necessary for their cancellation are derived. Global anomalies are shown to be connected with the differential characters of Cheeger and Simons. Their absence in sigma-models imposes restrictions on the target space that are also detailed.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 53B50
Mathematics Subject Classification ID: 81T60
zbMATH DE Number: 4069780
zbMATH Keywords: local anomalies
zbMATH Keywords: sigma-models
zbMATH Keywords: strings
zbMATH Keywords: global anomalies
zbMATH Keywords: field theories
zbMATH Keywords: evaluation map
author: L. Bonora
author: Paolo Cotta-Ramusino
author: M. Rinaldi
author: Jim Stasheff
reviewed by: Helmut Rumpf
MaRDI profile type: Publication
Wikidata QID: Q64038615
cites work: The evaluation map in field theory, sigma-models and strings. I
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: The aetiology of sigma model anomalies
cites work: Q5731354
cites work: Q3871594
cites work: Q5825483
cites work: The Yang-Mills equations over Riemann surfaces
cites work: Non-Abelian bosonization in two dimensions
cites work: Characteristic forms and geometric invariants
cites work: Q3739937
cites work: Q4061677
cites work: Complex manifolds without potential theory. (With an appendix on the geometry of characteristic classes). 2nd ed
cites work: Weyl cocycles
cites work: Q4195061
cites work: Q3692043
cites work: On the Weil-Petersson Metric on Teichmuller Space
cites work: Differentiable imbeddings
cites work: Plongements différentiables de variétés dans variétés
cites work: Effective field theory from quantized strings
cites work: Spinors and diffeomorphisms
cites work: Q4046802
cites work: Q3734212
cites work: Global gravitational anomalies
cites work: Determinants, torsion, and strings
cites work: The chiral determinant and the eta invariant
cites work: Q4746669
cites work: Q3757004
cites work: Differential characters: The Dirac monopole as an example
cites work: Existence of Universal Connections
cites work: Dirac operators coupled to vector potentials
cites work: Q3793324
cites work: On manifolds homeomorphic to the 7-sphere
cites work: The transversality characteristic class and linking cycles in surgery theory
cites work: Spectral asymmetry and Riemannian Geometry. I
cites work: Q3288660
cites work: Q3726964
cites work: Some remarks on BRS transformations, anomalies and the cohomology of the Lie algebra of the group of gauge transformations
full work available at URL: https://doi.org/10.1007/bf01242137
OpenAlex ID: W4244629463
Recommended article: The evaluation map in field theory, sigma-models and strings. I
Recommended article: Q3769582
Recommended article: Fermions and anomalies in quantum field theories
Recommended article: Q4251646
Recommended article: Global gravitational anomalies
Recommended article: Q3785567
Recommended article: The aetiology of sigma model anomalies
Recommended article: A note on global gauge anomalies.
Recommended article: Global anomalies, string theory and spacetime topology
Recommended article: Algebraic study of chiral anomalities
description: scientific article; zbMATH DE number 4069780