More on the properties of the first Gribov region in Landau gauge

TL;DR

This paper investigates the structure of the first Gribov region in Landau gauge for SU(2) Yang-Mills theory across multiple dimensions using lattice gauge theory, aiming to improve the comparison of gauge-dependent quantities.

Contribution

It provides a detailed lattice study of the first Gribov region in Landau gauge across different dimensions and volumes, addressing gauge-fixing ambiguities.

Findings

Structure of the first Gribov region characterized in 2D, 3D, and 4D.

Insights into the volume and discretization dependence of the region.

Enhanced understanding of gauge-fixing ambiguities in non-Abelian gauge theories.

Abstract

Complete gauge-fixing beyond perturbation theory in non-Abelian gauge theories is a non-trivial problem. This is particularly evident in covariant gauges, where the Gribov-Singer ambiguity gives an explicit formulation of the problem. In practice, this is a problem if gauge-dependent quantities between different methods, especially lattice and continuum methods, should be compared: Only when treating the Gribov-Singer ambiguity in the same way is the comparison meaningful. To provide a better basis for such a comparison the structure of the first Gribov region in Landau gauge, a subset of all possible gauge copies satisfying the perturbative Landau gauge condition, will be investigated. To this end, lattice gauge theory will be used to investigate a two-dimensional projection of the region for SU(2) Yang-Mills theory in two, three, and four dimensions for a wide range of volumes and discretizations.