The static quark potential from the gauge invariant Abelian decomposition (original) (raw)
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We prove Abelian magnetic monopole dominance in the string tension of QCD. Abelian and monopole dominance in low energy physics of QCD has been confirmed for various quantities by recent Monte Carlo simulations of lattice gauge theory. In order to prove this dominance, we use the reformulation of continuum Yang-Mills theory in the maximal Abelian gauge as a deformation of a topological field theory of magnetic monopoles, which was proposed in the previous article by the author. This reformulation provides an efficient way for incorporating the magnetic monopole configuration as a topological non-trivial configuration in the functional integral. We derive a version of the non-Abelian Stokes theorem and use it to estimate the expectation value of the Wilson loop. This clearly exhibits the role played by the magnetic monopole as an origin of the Berry phase in the calculation of the Wilson loop in the manifestly gauge invariant manner. We show that the string tension derived from the diagonal (abelian) Wilson loop in the topological field theory (studied in the previous article) converges to that of the full non-Abelian Wilson loop in the limit of large Wilson loop. Therefore, within the above reformulation of QCD, this result (together with the previous result) completes the proof of quark confinement in QCD based on the criterion of the area law of the full non-Abelian Wilson loop.
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Based on the dual-superconductor picture, we study the confinement physics in QCD in terms of the monopole in the maximally abelian (MA) gauge using the SU(2) lattice QCD. In the MA gauge, the off-diagonal gluon component is forced to be small, and hence microscopic abelian dominance on the link variable is observed in the lattice QCD for the whole region of beta\betabeta. From the gluon-propagator analysis in the lattice QCD, the origin of abelian dominance for the long-range physics is interpreted as the effective mass mchsimeq0.9rmGeVm_{ch} \simeq 0.9 {\rm GeV}mchsimeq0.9rmGeV of the charged gluon induced by the MA gauge fixing. In the MA gauge, there appears the macroscopic network of the monopole world-line covering the whole system, which would be identified as monopole condensation at a large scale. Using the dual Wilson loop in the MA gauge, we find the effective mass of the dual gluon field, mBsimeqm_B \simeq mBsimeq0.5GeV, which is the evidence of the dual Higgs mechanism by monopole condensation. The large fluctuation ...
Non-Abelian Stokes Theorem and Quark Confinement in SU(3) Yang–Mills Gauge Theory
Modern Physics Letters A, 2000
We derive a new version of SU (3) non-Abelian Stokes theorem by making use of the coherent state representation on the coset space SU (3)/ U (1) × U (1)) = F2, the flag space. Then we outline a derivation of the area law of the Wilson loop in SU (3) Yang–Mills theory in the maximal Abelian gauge (the detailed exposition will be given in a forthcoming article). This derivation is performed by combining the non-Abelian Stokes theorem with the reformulation of the Yang–Mills theory as a perturbative deformation of a topological field theory recently proposed by one of the authors. Within this framework, we show that the fundamental quark is confined even if G = SU (3) is broken by partial gauge fixing into H = U (2) just as G is broken to H = U(1) × U(1). An origin of the area law is related to the geometric phase of the Wilczek–Zee holonomy for U (2). Abelian dominance is an immediate by-product of these results and magnetic monopole plays the dominant role in this derivation.
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Canadian Journal of Physics, 2002
Using the magnetic symmetry structure of non-Abelian gauge theories of the YangMills type, the mathematical foundation of dual chromodynamics in fiber-bundle form is discussed. The dual gauge potential in its restricted form is constructed in terms of magnetic vectors on global sections, which has been shown to lead the dual dynamics between topological charges and color isocharges. Constructing the Lagrangian for such dual theory, the dynamical breaking of magnetic symmetry by an effective potential is shown to push the QCD vacuum in a confining phase. The dynamical structure of the theory is investigated by deriving the field equations associated with the confining phase. The associated flux-tube structure responsible for the confinement is analyzed by computing the asymptotic string solutions of the field equations under cylindrical symmetry. Using the confining part of the dual restricted Lagrangian, the finite string energy per unit length is calculated and its implications on...