Gribov horizon and Gribov copies effect in lattice Coulomb gauge
arXiv:1608.05795 · doi:10.1103/PhysRevD.95.014503
Abstract
Following a recent proposal by Cooper and Zwanziger we investigate via lattice simulations the effect on the Coulomb gauge propagators and on the Gribov-Zwanziger confinement mechanism of selecting the Gribov copy with the smallest non-trivial eigenvalue of the Faddeev-Popov operator, i.e.~the one closest to the Gribov horizon. Although such choice of gauge drives the ghost propagator towards the prediction of continuum calculations, we find that it actually overshoots the goal. With increasing computer time, we observe that Gribov copies with arbitrarily small eigenvalues can be found. For such a method to work one would therefore need further restrictions on the gauge condition to isolate the physically relevant copies, since e.g.~the Coulomb potential defined through the Faddeev-Popov operator becomes otherwise physically meaningless. Interestingly, the Coulomb potential alternatively defined through temporal link correlators is only marginally affected by the smallness of the eigenvalues.
arXiv comment11 pages, 13 figures. Discussion and conclusions extended, some plots changed. To appear in PRD
References in corpus (41)
- Coulomb Gauge QCD, Confinement, and the Constituent Representation
- Variational solution of the Yang-Mills Schrödinger equation in Coulomb gauge
- Modeling the Gluon Propagator in Landau Gauge: Lattice Estimates of Pole Masses and Dimension-Two Condensates
- Three-point vertices in Landau-gauge Yang-Mills theory
- No confinement without Coulomb confinement
- On the Yang-Mills wave functional in Coulomb gauge
- Confining Solution of the Dyson-Schwinger Equations in Coulomb Gauge
- Coulomb gauge gluon propagator and the Gribov formula
- Constructing non-perturbative gauges using correlation functions
- More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
- Infrared analysis of propagators and vertices of Yang--Mills theory in Landau and Coulomb gauge
- Lattice evidence for the family of decoupling solutions of Landau gauge Yang-Mills theory
- Improved Landau gauge fixing and the suppression of finite-volume effects of the lattice gluon propagator
- Landau gauge ghost and gluon propagators in SU(2) lattice gauge theory: Gribov ambiguity revisited
- Center Vortices and the Gribov Horizon
- Dielectric function of the QCD vacuum
- Enumerating Gribov copies on the lattice
- The effective Coulomb potential in SU(3) lattice Yang-Mills theory
- BRST symmetry vs. Horizon condition in Yang-Mills theories
- Coulomb, Landau and Maximally Abelian Gauge Fixing in Lattice QCD with Multi-GPUs
- Hamiltonian Flow in Coulomb Gauge Yang-Mills Theory
- Running mass, effective energy and confinement: the lattice quark propagator in Coulomb gauge
- Coulomb vs. physical string tension on the lattice
- Numerical Study of the Fundamental Modular Region in the Minimal Landau Gauge
- The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition
- The role of center vortices in Gribov's confinement scenario
- Ghost propagator and the Coulomb form factor from the lattice
- Vertex functions of Coulomb gauge Yang--Mills theory
- The String Tension in Gauge Theories: a Suggestion for a New Measurement Method
- More on the properties of the first Gribov region in Landau gauge
- Enumerating Copies in the First Gribov Region on the Lattice in up to four Dimensions
- Gauge Theories on a 2+2 Anisotropic Lattice
- Modified SO(3) Lattice Gauge Theory at non zero T with Parallel Tempering: Monopole and Vortex Condensation
- Universality, vortices and confinement: modified SO(3) lattice gauge theory at non-zero temperature
- On the temporal Wilson loop in the Hamiltonian approach in Coulomb gauge
- A finite temperature investigation of dual superconductivity in the modified SO(3) lattice gauge theory
- Vortex free energy and deconfinement in center-blind discretizations of Yang-Mills theories
- Origin of Confining Force
- Fixed twist dynamics of SO(3) gauge theory
- Gauge Orbits and the Coulomb Potential
- Topological order and the vacuum of Yang-Mills theories