The gauging of two-dimensional bosonic sigma models on world-sheets with defects

We extend our analysis of the gauging of rigid symmetries in bosonic two-dimensional sigma models with Wess-Zumino terms in the action to the case of world-sheets with defects. A structure that permits a non-anomalous coupling of such sigma models to world-sheet gauge fields of arbitrary topology is analysed, together with obstructions to its existence, and the classification of its inequivalent choices.