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Global gauge anomalies in two-dimensional bosonic sigma models. (English) Zbl 1213.81167
Gauge invariance constitutes one of the basic principles underlying the theoretical description of physical reality. The occurrence of gauge anomalies in some models of quantum field theory with chiral fermions yields a powerful selection principle for the model building in high energy physics. Gauge anomalies may describe violations of infinitesimal gauge invariance. In other words they describe the breakdown of invariance under large gauge transformations not homotopic to identity. The authors of this interesting paper revisit the gauging of symmetries in two-dimensional bosonic sigma models with a Wess-Zumino term in the action. Such a term is related to a background closed 3-form \(H\) on the target space. It is known that under some conditions the classical amplitudes may be coupled to the topologically trivial gauge fields of the symmetry group in a way assures infinitesimal gauge invariance. The authors show that the resulting gauged Wess-Zumino amplitudes may, nevertheless, exhibit global gauge anomalies which can be classified. The general results are illustrated on the example of the WZW and the coset models of conformal field theory. It is introduced the notion of equivariant gerbes that allow an anomaly-free coupling of the Wess-Zumino amplitudes to all gauge fields, including the ones in non-trivial principal bundles. An explicit construction of gerbes equivariant with respect to the adjoint symmetries over compact simply connected simple Lie groups is discussed.

MSC:
81T10 Model quantum field theories
81T13 Yang-Mills and other gauge theories in quantum field theory
81T18 Feynman diagrams
81T50 Anomalies in quantum field theory
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