Center vortices and the SU(3) conformal window

A novel approach for estimating the lower end of the SU(3) conformal window is presented through the study of center vortex geometry and its dependence on the number of fermion flavors Nf. Values ranging from Nf = 2-8 are utilized to infer an upper limit for vortex behavior in the low Nf phase, which may inform the transition to the conformal window. The simulations are performed at a single lattice spacing and pion mass, both fixed for all Nf. Visualizations of the center vortex structure in three-dimensional slices of the lattice reveal a growing roughness in the vortex matter as a function of Nf, embodied by an increase in the density of vortex matter in the percolating cluster and a simultaneous reduction in secondary clusters disconnected from the percolating cluster in 3D slices. This is quantified by various bulk properties, including the vortex and branching point densities. A correlation of the vortex structure reveals a turning point near Nf similar or equal to 5 past which a randomness in the vortex field becomes the dominant aspect of its evolution with Nf. As a byproduct, extrapolations to the vortex content of a uniform-random gauge field provide a critical point at which there must be a drastic shift in vacuum field structure. A precise estimate for the critical value is extracted as Nf = 11.43(16)(17), close to various other estimates.