Confinement in QCD and generic Yang-Mills theories with matter representations

TL;DR

This paper demonstrates that in the large N limit of QCD, quark confinement emerges through a phase transition in a non-local NJL model, with implications for the physical spectrum of quarks.

Contribution

It derives the low-energy limit of QCD in the 't Hooft limit, showing confinement via a phase transition in a non-local NJL model influenced by instanton effects.

Findings

Quark confinement is recovered in the 't Hooft limit.

A phase transition from chiral condensate to instanton liquid occurs as coupling increases.

Quark propagator poles move to the complex plane, indicating confinement.

Abstract

We derive the low-energy limit of quantum chromodynamics (QCD) and provide evidence that in the 't Hooft limit, i.e. for a very large number of colors and increasing 't Hooft coupling, quark confinement is recovered. The low energy limit of the theory turns out to be a non-local Nambu-Jona-Lasinio (NJL) model. The effect of non-locality, arising from a gluon propagator that fits quite well to the profile of an instanton liquid, is to produce a phase transition from a chiral condensate to an instanton liquid, as the coupling increases with lower momentum. This phase transition suffices to move the poles of the quark propagator to the complex plane. As a consequence, free quarks are no longer physical states in the spectrum of the theory.