Bounds on free energy in QCD

Abstract

We derive some exact bounds on the free energy $W(J)$ in QCD, where $J_{\mu }^b$ is a source for the gluon field $A_{\mu }^b$ 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, $\frac{\partial W(h)}{\partial h}=0,$ 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.

Comments: 8 pages, 3 figures, Conference: Xth Quark Confinement and the Hadron Spectrum, October 8-12, 2012, TUM Campus Garching, Munich, Germany