The static quark potential from the gauge invariant Abelian decomposition

Abstract

We investigate the relationship between colour confinement and topological structures derived from the gauge invariant Abelian (Cho-Duan-Ge) decomposition. This Abelian decomposition is made imposing an isometry on a colour field $n$ which selects the Abelian direction; the principle novelty of our study is that we have defined this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path ordered integral of the non-Abelian gauge fields with an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. By using Stokes' theorem, we can relate the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by topological structures, which occur when one of the parameters parametrising the colour field $n$ winds itself around a non-analyticity in the colour field. If they exist, these objects will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and find that the restricted field strength is dominated by peaks on the lattice. Wilson Loops containing these peaks show a stronger area-Law and thus provide the dominant contribution to the string tension.

8 pages, 3 figures; v2 some minor changes (including updated numerical results), accepted for publication in Physics Letters

References in corpus (9)

• Trivializing maps, the Wilson flow and the HMC algorithm
• Over-Improved Stout-Link Smearing
• Wilson loop and magnetic monopole through a non-Abelian Stokes theorem
• Non-Abelian Dual Superconductor Picture for Quark Confinement
• Dimensional Transmutation by Monopole Condensation in QCD
• Low-lying Wilson Dirac operator eigenvector mixing in dynamical overlap Hybrid Monte-Carlo
• The exact decomposition of gauge variables in lattice Yang-Mills theory
• Topological configurations of Yang-Mills field responsible for magnetic-monopole loops as quark confiner
• String tension from gauge invariant Magnetic Monopoles

Cited by in corpus (6)

• Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory
• The Static Quark Potential from the Gauge Independent Abelian Decomposition
• Abelian Decomposition and Glueball-Quarkonium Mixing in QCD
• Abelian Decomposition and Weyl Symmetric Effective Action of SU(3) QCD
• Experimental Verification of Two types of Gluon Jets in QCD
• Complete Monopole Dominance of the Yang-Mills Confining Potential