The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition

Abstract

We study gauge fixing via the standard local extremization algorithm for 2-dimensional $U(1)$. On a lattice with spherical topology $S^2$ where all copies are lattice artifacts, we find that the number of these 'Gribov' copies diverges in the continuum limit. On a torus, we show that lattice artifacts can lead to the wrong evaluation of the gauge-invariant correlation length, when measured via a gauge-fixed procedure; this bias does not disappear in the continuum limit. We then present a new global approach, based on Hodge decomposition of the gauge field, which produces a unique smooth field in Landau gauge, and is economically powered by the FFT. We also discuss the use of this method for examining topological objects, and its extensions to non-abelian gauge fields.

6 pages, uuencoded postscript, presented at Lattice 94

References in corpus (3)

• Gauge Fixing on the Lattice without Ambiguity
• Dirac sheets and gauge fixing in $U(1)$ lattice gauge theory
• The First Order Signal in Pure U(1) Gauge Theory May be Fake

Cited by in corpus (21)

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• More on Gribov copies and propagators in Landau-gauge Yang-Mills theory
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• Infrared Behavior of the Gluon Propagator in Lattice Landau Gauge
• Instantons and Gribov Copies in the Maximally Abelian Gauge
• Lattice Chiral Fermions
• Equivariant Gauge Fixing of SU(2) Lattice Gauge Theory
• Lorentz gauge and Gribov ambiguity in the compact lattice U(1) theory
• Gribov Problem for Gauge Theories: a Pedagogical Introduction
• Dependence of the propagators on the sampling of Gribov copies inside the first Gribov region of Landau gauge
• 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
• Gribov horizon and Gribov copies effect in lattice Coulomb gauge
• Laplacian gauge and instantons
• Fermionic correlators and zero-momentum modes in quenched lattice QED
• More on Lattice BRST Invariance
• Non-perturbative Renormalization of Lattice Operators
• Gribov Copy and Complex Phase of Chiral Determinant
• Hodge gauge fixing in three dimensions
• Gauge invariant investigation of the nature of Confinement