Condition for confinement in non-Abelian gauge theories

Abstract

We show that a criterion for confinement, based on the BRST invariance, holds in four dimensions, by solving a non-Abelian gauge theory with a set of exact solutions. The confinement condition we consider was obtained by Kugo and Ojima some decades ago. The current understanding of gauge theories permits us to apply the techniques straightforwardly for checking the validity of this criterion. In this way, we are able to show that the non-Abelian gauge theory is confining and that confinement is rooted in the BRST invariance and asymptotic freedom.

Diluted mass gap in strongly coupled non-local Yang-Mills

“…This is a rather interesting result in view of the Kugo-Ojima criterion for confinement in a Yang-Mills theory without fermions [69,70]. It was shown recently that this criterion, obtained by BRST invariance, provides the exact beta function for the local theory that is shown to confine [71]. Therefore, we are in a very similar situation in the non-local case and we could get a beta function, even if approximately, describing the behaviour of the theory on all the energy range providing a confinement proof.…”

Differential Dyson–Schwinger equations for quantum chromodynamics

“…Quite recently, the set of Dyson-Schwinger equations for this case was solved, for the 1-and 2-point functions, and the spectrum very-well a e-mail: marcofrasca@mclink.it (corresponding author) accurately computed both in 3 and 4 dimensions [13][14][15]. Confinement was also proved to be a property of the theory [14,16].…”

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

“…A proof of confinement exists in supersymmetric models where a condensate of monopoles like in a type II superconductors is seen [10,11]. Indeed, the exact β function for the Yang-Mills theory both for the supersymmetric and the non-supersymmetric case is known [12][13][14]. Different confinement criteria and their overlapping regions are presented in Ref.…”