Bounds on free energy in QCD

We derive some exact bounds on the free energy W(J) in QCD, where J _μ^b is a source for the gluon field A _μ^b in the minimal Landau gauge, andW(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.