Ghost sector and geometry in minimal Landau gauge: further constraining the infinite-volume limit

Abstract

We present improved upper and lower bounds for the momentum-space ghost propagator of Yang-Mills theories in terms of the two smallest nonzero eigenvalues (and their corresponding eigenvectors) of the Faddeev-Popov matrix. These results are verified using data from four-dimensional numerical simulations of SU(2) lattice gauge theory in minimal Landau gauge at beta = 2.2, for lattice sides N = 16, 32, 48 and 64. Gribov-copy effects are discussed by considering four different sets of numerical minima. We then present a lower bound for the smallest nonzero eigenvalue of the Faddeev-Popov matrix in terms of the smallest nonzero momentum on the lattice and of a parameter characterizing the geometry of the first Gribov region $\Omega$. This allows a simple and intuitive description of the infinite-volume limit in the ghost sector. In particular, we show how nonperturbative effects may be quantified by the rate at which typical thermalized and gauge-fixed configurations approach the boundary of Omega, known as the first Gribov horizon. As a result, a simple and concrete explanation emerges for why lattice studies do not observe an enhanced ghost propagator in the deep infrared limit. Most of the simulations have been performed on the Blue Gene/P--IBM supercomputer shared by Rice University and São Paulo University.

30 pages, 16 figures (40 plots), 2 tables; minor modifications; final version to appear in Physical Review D

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Cited by in corpus (16)

• The three-gluon vertex in Landau gauge
• Lattice Gluon and Ghost Propagators, and the Strong Coupling in Pure SU(3) Yang-Mills Theory: Finite Lattice Spacing and Volume Effects
• More on the non-perturbative Gribov-Zwanziger quantization of linear covariant gauges
• On mass generation in Landau-gauge Yang-Mills theory
• The (IR-)relevance of the Gribov ambiguity in SU(2) x U(1) gauge theories with fundamental Higgs matter
• On bounds and boundary conditions in the continuum Landau gauge
• Reply to "Comment on 'Lattice Gluon and Ghost Propagators, and the Strong Coupling in Pure SU(3) Yang-Mills Theory: Finite Lattice Spacing and Volume Effects' "
• More on the properties of the first Gribov region in Landau gauge
• Accessing the topological susceptibility via the Gribov horizon
• Bloch Waves in Minimal Landau Gauge and the Infinite-Volume Limit of Lattice Gauge Theory
• Natural solution in the refined Gribov-Zwanziger theory
• Lorentz symmetry breaking in a Yang-Mills theory within the Gribov restriction
• Non-Abelian extension of the aether term and the Gribov problem
• Crossing the Gribov horizon: an unconventional study of geometric properties of gauge-configuration space in Landau gauge
• Lattice oscillator model on noncommutative space: eigenvalues problem for the perturbation theory
• Complex Chern-Simons and Gribov