Detecting topological sectors in continuum Yang-Mills theory and the fate of BRST symmetry

In this work, motivated by Laplacian type center gauges in the lattice, designed to avoid the Gribov problem, we introduce a new family of gauge fixings for pure Yang-Mills theories in the continuum. This procedure separates the partition function into partial contributions associated with different sectors, containing center vortices and correlated monopoles. We show that, on each sector, the gauge fixed path integral displays a BRST symmetry. However, it cannot be globally extended due to sector-dependent boundary conditions on the ghost fields. These are nice features as they would permit us to discuss the independence of the partial contributions on gauge parameters, while opening a window for the space of quantum states to be different from the perturbative one, which would be implied if topological configurations were removed.