Renormalization constant of the color gauge field as a probe of confinement

Abstract

The mechanism of color confinement as a consequence of an unbroken non-abelian gauge symmetry and asymptotic freedom is elucidated and compared with that of other models based on an analogy with the type II superconductor. It is demonstrated that a sufficient condition for color confinement is given by Z −1 3 = 0 where Z 3 denotes the renormalization constant of the color gauge field. It is shown that this condition is actually satisfied in quantum chromodynamics and that some of the characteristic features of other models follow from it.

Condition for confinement in non-Abelian gauge theories

“…In this section we present the approach to confinement proposed in [4][5][6][7][8] and show how this reduces to the Kugo-Ojima criterion [3]. We emphasize that our proof is for the theory without fermions.…”

“…Here σ 0 is an integration constant having the dimension of mass. It is easy to see how this propagator recovers asymptotic freedom [4][5][6][7][8]. In the high-energy limit, we make the momenta run to infinity.…”

“…For example, Kugo and Ojima proposed a condition from BRST invariance based on charge annihilation [2,3]. On a similar ground, Nishijima and collaborators [4][5][6][7][8] obtained a constraint on the amplitudes of unphysical states signaling confinement. These authors showed that colour confinement arises as a consequence of BRST invariance and asymptotic freedom.…”

“…In this paper, we will apply the condition derived in [4][5][6][7][8], reducing it to the case of the Kugo-Ojima criterion [3], when, for a non-Abelian gauge theory without fermions, we start with known exact solutions to solve it [24]. In this way, the propagators of the theory are known and we can evaluate the behavior of the poles.…”

Two loop effective potential for langleA2μrangle in the Landau gauge in quantum chromodynamics

“…This would suggest that it has to be positive for a bounded potential and clearly this cannot occur in the case of quantum electrodynamics, (QED). Moreover, there has been renormalization group studies of the relation of this particular coefficient of the gluon anomalous dimension in connection with confinement, [54,55]. Thus, it is curious that a positivity condition emerges on the one loop Landau gauge anomalous dimension in the effective potential of a composite operator which has the dimensions of mass since the presence of a mass gap in QCD is indicative of confinement.…”