Spectral sum for the color-Coulomb potential in SU(3) Coulomb gauge lattice Yang-Mills theory

Y. Nakagawa, A. Nakamura, T. Saito, and H. Toki
Phys. Rev. D 81, 054509 – Published 24 March 2010

Abstract

We discuss the essential role of the low-lying eigenmodes of the Faddeev-Popov (FP) ghost operator on the confining color-Coulomb potential using SU(3) quenched lattice simulations in the Coulomb gauge. The color-Coulomb potential is expressed as a spectral sum of the FP ghost operator and has been explored by partially summing the FP eigenmodes. We take into account the Gribov copy effects that have a great impact on the FP eigenvalues and the color-Coulomb potential. We observe that the lowest eigenvalue vanishes in the thermodynamic limit much faster than that in the Landau gauge. The color-Coulomb potential at large distances is governed by the near-zero FP eigenmodes; in particular, the lowest one accounts for a substantial portion of the color-Coulomb string tension comparable to the Wilson string tension.

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  • Received 25 September 2008

DOI:https://doi.org/10.1103/PhysRevD.81.054509

©2010 American Physical Society

Authors & Affiliations

Y. Nakagawa1, A. Nakamura1, T. Saito2, and H. Toki3

  • 1Research Institute for Information Science and Education, Hiroshima University, Higashi-Hiroshima, Hiroshima, 739-8521, Japan
  • 2Integrated Information Center, Kochi University, Kochi, 780-8520, Japan
  • 3Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka, 567-0047, Japan

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Issue

Vol. 81, Iss. 5 — 1 March 2010

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