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

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.

19 pages, 1 figure. Version accepted for publication in Physics Letters B

References in corpus (13)

• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• Lattice gluodynamics computation of Landau-gauge Green's functions in the deep infrared
• Supersymmetry Inspired QCD Beta Function
• Infrared Gluon and Ghost Propagators
• On covariant nonlocal chiral quark models with separable interactions
• Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical Case
• On the analytic structure of scalar glueball operators at Born level
• Di-Gluonium Sum Rules, I = 0 Scalar Mesons and Conformal Anomaly
• On a novel evalutation of the hadronic contribution to the muon's $g-2$ from QCD
• Nambu-Jona-Lasinio model correlation functions from QCD
• $\Lambda$ parameter of the SU(3) Yang-Mills theory from the continuous $\beta$ function
• Gauge-Dependence of Green's Functions in QCD and QED
• Finite temperature corrections to a NLO Nambu-Jona-Lasinio model

Cited by in corpus (11)

• Fate of False Vacuum in Non-perturbative Regimes
• Fate of the false vacuum in string-inspired nonlocal field theory
• Dynamical generation of electroweak scale from the conformal sector: A strongly coupled Higgs via the Dyson--Schwinger approach
• Effective potential in non-perturbative gauge theories
• Mass gap in non-perturbative quadratic ${\mathcal{R}}^2$ gravity via Dyson-Schwinger
• Fate of false vacuum in non-perturbative regimes: Gravity effects
• Non-perturbative Origin of the Electroweak Scale: RGE in Strongly-coupled Dark Gauge Theories via Dyson-Schwinger
• Finite temperature QCD crossover at non-zero chemical potential: A Dyson-Schwinger approach
• Non-perturbative Origin of Electroweak Scale via Higgs-portal: Dyson-Schwinger in Conformally Invariant Scalar Sector
• Review of strongly coupled regimes in gravity with Dyson-Schwinger approach
• Renormalisable Non-local Quark-Gluon Interaction: Mass Gap, Chiral Symmetry Breaking & Scale Invariance