Studying the renormalizability of Yang-Mills theory in center-vortex sectors

In this work, we analyzed a recent proposal to detect $SU(N)$ continuum Yang-Mills sectors labeled by center vortices, inspired by Laplacian-type center gauges in the lattice. Initially, after the introduction of appropriate external sources, we obtained a rich set of sector-dependent Ward identities, which can be used to control the form of the divergences. Next, we were able to show the all-order multiplicative renormalizability of the center-vortex free sector. These are important steps towards the establishment of a first principles, well-defined, and calculable Yang-Mills ensemble.