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Non-Abelian Stokes Theorem and Quark Confinement in SU(3) Yang-Mills Gauge Theory

Abstract

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))=F2SU(3)/(U(1)\times U(1))=F_2, 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)G=SU(3) is broken by partial gauge fixing into H=U(2)H=U(2) just as GG is broken to H=U(1)×U(1)H=U(1) \times 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 byproduct of these results and magnetic monopole plays the dominant role in this derivation.Comment: 14 pages, Latex, no figures, version accepted for publication in Mod. Phys. Lett. A (some comments are added in the final parts

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