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Decomposition of the static potential in SU(3) gluodynamics

V. G. Bornyakov, I. Kudrov

TL;DR

This paper extends the SU(2) lattice result that the static potential can be decomposed into a monopole (linear) and a monopoleless (Coulomb) part to SU(3) in the Maximal Abelian Gauge. By performing MAG fixing, Abelian projection, and a monopole decomposition built from Dirac plaquettes, the authors compute the non-Abelian, Abelian-monopole, and monopoleless potentials from Wilson loops. They find $V(R) \approx V_{mon}(R) + V_{mod}(R)$ across distances, with $V_{mon}(R)$ linear and $V_{mod}(R)$ Coulomb-like, and only a ~10% mismatch at large $R$ for their lattice setup, improving toward the continuum. The results support Abelian and monopole dominance in SU(3) and highlight the monopole-plus-monopoleless decomposition as a robust description, while noting gauge-fixing quality and the continuum limit as important future directions.

Abstract

After fixing the Maximal Abelian gauge in SU(3) lattice gluodynamics we decompose the nonabelian gauge field into the Abelian field created by Abelian monopoles and the modified nonabelian field with monopoles removed. We then calculate respective static potentials in the fundamental representation and show that the sum of these potentials approximates the nonabelian static potential with good precision at all distances considered. Comparison with other ways of decomposition is made.

Decomposition of the static potential in SU(3) gluodynamics

TL;DR

This paper extends the SU(2) lattice result that the static potential can be decomposed into a monopole (linear) and a monopoleless (Coulomb) part to SU(3) in the Maximal Abelian Gauge. By performing MAG fixing, Abelian projection, and a monopole decomposition built from Dirac plaquettes, the authors compute the non-Abelian, Abelian-monopole, and monopoleless potentials from Wilson loops. They find across distances, with linear and Coulomb-like, and only a ~10% mismatch at large for their lattice setup, improving toward the continuum. The results support Abelian and monopole dominance in SU(3) and highlight the monopole-plus-monopoleless decomposition as a robust description, while noting gauge-fixing quality and the continuum limit as important future directions.

Abstract

After fixing the Maximal Abelian gauge in SU(3) lattice gluodynamics we decompose the nonabelian gauge field into the Abelian field created by Abelian monopoles and the modified nonabelian field with monopoles removed. We then calculate respective static potentials in the fundamental representation and show that the sum of these potentials approximates the nonabelian static potential with good precision at all distances considered. Comparison with other ways of decomposition is made.
Paper Structure (4 sections, 15 equations, 2 figures, 1 table)

This paper contains 4 sections, 15 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Decomposition of the gauge field
  3. The static potential decomposition
  4. Conclusions

Figures (2)

  • Figure 1: Fig 1. Comparison of the nonabelian potential $V(R)$ (filled circles) with the sum $V_{mod}(R)+V_{mon}(R)$ (filled triangles) for $\beta=6.0$. $V_{mod}(r)$ (empty circles) and $V_{mon}(r)$ (filled inverted triangles) are also depicted. The solid curves show the fits to the Cornell potential.
  • Figure 2: Fig 2. Comparison of the nonabelian potential $V(R)$ (filled circles) with the sum $V_{mod}(R)+V_{mon}(R)$ (filled inverted triangles) and the sum $V_{Abel}(R)+V_{offd}(R)$ (filled squares). $V_{offd}(r)$ (filled triangles) and $V_{Abel}(r)$ (empty circles) are also depicted. The solid curves show the fits to the Cornell potential.