Validity of the diffusion-to-viscosity ratio bounds

Determine whether the ratio \((2\pi T D_s)/(4\pi \eta/s)\) is confined between 1 and \(5/2\) as the interaction changes from the strong-coupling regime to the weak-coupling regime.

Background

The thesis introduces $(2\pi T D_s)/(4\pi\eta/s)$ as a proposed diagnostic for the coupling regime of hot QCD. The lower value 1 is associated with the strongly coupled AdS/CFT estimate, while the upper value $5/2$ follows from a weakly coupled kinetic-theory estimate under additional approximations. The stated range is explicitly characterized as a conjecture. Later calculations in the Quasi-Particle Model indicate that the ratio may fall below 1 and that the approximations underlying the proposed weak-coupling limit are not quantitatively reliable, leaving the general validity of the conjectured interval unresolved.