Bounds on free energy in QCD

TL;DR

This paper establishes exact bounds on the free energy in QCD with a static gluon source, revealing the system's insensitivity to static color probes and providing numerical validation of these bounds.

Contribution

It derives new exact bounds on the QCD free energy in the minimal Landau gauge, showing the system's lack of response to static sources and numerically confirming the bounds.

Findings

Free energy vanishes for static sources, $W(h) = 0$.

System does not respond to static color probes.

Numerical evaluations confirm bounds are satisfied and undersaturated.

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, ${\partial W(h) \over \partial h} = 0,$ 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.