Background independence in gauge theories

Classical field theory is background independent in the sense that it is insensitive to the split of the field into a background configuration and a dynamical perturbation. At the quantum level, we define background independent observables in a geometrical formulation as flat sections of the observable algebra bundle over the manifold of background configurations, with respect to a flat connection which implements background variations. A QFT is then called background independent if such a flat (Fedosov) connection exists. We analyze the obstructions to preserve background independence at the quantum level for pure Yang-Mills theory and show that all potential obstructions can be removed by finite renormalization. We also comment on the background-independence of perturbative quantum gravity. Joint work with Jochen Zahn. Based on arXiv:1804.07640.