ar X iv : h ep - l at / 9 71 20 27 v 2 2 5 D ec 1 99 7 Dual Wilson loop and inter - monopole potential in lattice QCD

We study the dual Wilson loop and the inter-monopole potential(the static potential between the color magnetic monopoles) in the maximally abelian gauge to clarify the dual Higgs mechanism induced by monopole condensation. There is no (color-)electric current in the monopole part, which includes the essence of the nonperturbative QCD, and hence the system can be described by the dual gauge field Bµ without the singularity like the Dirac string. We find that the dual Wilson loop seems to obey the perimeter law, and the inter-monopole potential becomes Yukawa-type in the infrared region. From the inter-monopole potential, we estimate the dual gluon mass m B and the effective size R of the monopole: m B ≃ 0.5GeV, R ≃ 0.35fm. We study the confinement mechanism in the nonperturbative QCD(NP-QCD) based on the dual superconductor picture. 1 In the dual superconductor scenario , the QCD vacuum is considered as the dual version of the supercon-ductor, and the dual Meissner effect, the exclusion of the color-electric field, is brought by condensation of the monopole with the color-magnetic charge instead of the Cooper-pair with the electric charge. As for the appearance of monopoles in QCD, QCD in the 'tHooft abelian gauge is reduced into an abelian gauge theory including monopole. 2,3,5 In the abelian gauge, only abelian gluon component is relevant for NP-QCD, and the abelian gauge variable can be separated into the photon part and the monopole part. NP-QCD are realized only in the monopole part. Since the monopole part in QCD dose not include the electric current j µ and only includes the magnetic monopole current, the system resembles the dual version of QED. Then, instead of the ordinary gauge field A µ we can introduce the dual gauge field B µ without the singularity like the Dirac string. The dual gauge field B µ satisfies ∂ µ B ν − ∂ ν B µ = * F µν = 1 2 ε µνρσ F ρσ , which is the dual version of the ordinary relation, F µν ≡ ∂ µ A ν − ∂ ν A µ. In the dual formalism, the absence of j ν is expressed as the dual Bianchi identity, j ν = ∂ µ F µν = ∂ µ * (∂ ∧ B) µν = 0. In terms of the dual Higgs mechanism, we expect that the inter-monopole potential is short-range Yukawa-type, and the dual gauge field …