Center vortices and the $\mathrm{SU}(3)$ conformal window

TL;DR

This study investigates the geometry of center vortices in SU(3) gauge theory across different fermion flavor numbers to estimate the lower boundary of the conformal window, revealing structural transitions near a critical flavor number.

Contribution

It introduces a novel vortex-based method to estimate the SU(3) conformal window's lower end, analyzing vortex structure dependence on fermion flavors at fixed lattice parameters.

Findings

Vortex roughness increases with N_f, indicating structural changes.

A critical flavor number N_f* ≈ 11.43 is identified, marking a shift in vacuum structure.

Vortex and branching point densities correlate with the transition to conformality.

Abstract

A novel approach for estimating the lower end of the $\mathrm{SU}(3)$ conformal window is presented through the study of center vortex geometry and its dependence on the number of fermion flavors $N_f$. Values ranging from $N_f = 2$--$8$ are utilized to infer an upper limit for vortex behavior in the low $N_f$ 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 $N_f$. 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 $N_f$, 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 $N_f \simeq 5$ past which a randomness in the vortex field becomes the dominant aspect of its evolution with $N_f$. 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 $N_f^* = 11.43(16)(17)$, close to various other estimates.