A model of color confinement

TL;DR

This paper introduces a simple model for QCD's free energy under an external plane wave current, aligning with bounds from the Gribov horizon and fitting lattice data that suggest non-analytic behavior at zero momentum.

Contribution

It presents a novel simple model of color confinement that incorporates Gribov horizon bounds and fits recent lattice data indicating non-analyticity in the free energy.

Findings

The model satisfies the Gribov horizon bound.

Lattice data favor non-analyticity in the free energy.

The model explains the non-zero gluon propagator at zero momentum.

Abstract

A simple model is presented that describes the free energy $W(J)$ of QCD coupled to an external current that is a single plane wave, $J(x) = H \cos(k \cdot x)$. The model satisfies a bound obtained previously on $W(J)$ that comes from the Gribov horizon. If one uses this model to fit recent lattice data --- which give for the gluon propagator $D(k)$ a non-zero value, $D(0) \neq 0$, at $k = 0$ --- the data favor a non-analyticity in $W(J)$.