Usefulness of the color fluctuation measure F_{R;ρ_phys} for understanding confinement

Determine whether analyses of F_{R;ρ_phys}—the ultraviolet-regularization-independent quantity constructed from the vacuum expectation of the squared net color charge in a spatial region R and its shift in a physical ensemble ρ_phys—can provide useful insights into the physics of color confinement in quantum chromodynamics (QCD).

Background

The paper proves that although the operator for the squared net color charge in a region, Q_R^2, is not gauge invariant, its expectation value in physical states is gauge invariant and necessarily nonzero; however, it depends on the regularization scheme and scale. To address ultraviolet issues, the author introduces F_{R;ρ_phys}, a specific combination of the vacuum expectation value of Q_R^2 and its shift in a nontrivial state or ensemble ρ_phys, which has a well-defined continuum limit.

The work analyzes the behavior of these color charge fluctuations and of F_{R;ρphys} in several settings (vacuum, thermal ensembles, and systems with static color sources connected by a flux tube). The observed area-scaling and other counterintuitive features challenge straightforward interpretations, motivating the explicit open question of whether studying F{R;ρ_phys} can ultimately yield meaningful insights into the physics of confinement.