Bounds on free energy in QCD

Abstract

We derive some exact bounds on the free energy W (J) in QCD, where J b µ is a source for the gluon field A b µ in the minimal Landau gauge, and W (J) is the generating functional of connected gluon correlators. Among other results, we show that for a static source J(x) = h the free energy vanishes, W (h) = 0, together with its first derivative, ∂W (h) ∂ h = 0, for all h, no matter how strong. Thus the system does not respond to a static color probe. We also present numerical evaluations of the free energy W (J) and find that the bounds are well satisfied and in fact undersaturated.