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The gauging of two-dimensional bosonic sigma models on world-sheets with defects. (English) Zbl 1278.81135
The procedure of the gauging of rigid symmetries in bosonic two-dimensional sigma models with Wess-Zumino terms in the action is extended to the case of world-sheets with defects. First, the mathematical structures involved in the definition of Feynman amplitudes of the sigma models with defects is recalled. Then, the coupling of the sigma model to gauge fields in a trivial principal bundle of the symmetry group is studied and an extension to the case of sigma models with defects is presented. The behavior of the gauged amplitudes under large and infinitesimal gauge transformations is analyzed and the Wess-Zumino-Witten with defects is given as an illustrative example. The conditions assuring the absence of local gauge anomalies are obtained. An extension of a \(G\)-equivariant structure on gerbes is realized in order to determine the Feynman amplitudes for a sigma model with defects. It is shown how a \(G\)-equivariant structure allows the coupling of the sigma model with defects to world-sheet gauge fields in an arbitrary principal \(G\)-bundle. The obstructions to the existence of \(G\)-equvariant structures is also provided and a classification of such structures is given. The technical proofs of the theorems formulated in this paper and some additional results are presented in detail in seven final Appendices.

MSC:
81T20 Quantum field theory on curved space or space-time backgrounds
53C08 Differential geometric aspects of gerbes and differential characters
81T50 Anomalies in quantum field theory
70S10 Symmetries and conservation laws in mechanics of particles and systems
81T13 Yang-Mills and other gauge theories in quantum field theory
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
55R91 Equivariant fiber spaces and bundles in algebraic topology
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