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

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.Comment: 42 pages, 23 figures, 1 tabl

Landau gauge Yang-Mills correlation functions

“…While the FRG computations lack apparent convergence in this regime, the lattice data are affected by the non-perturbative gauge fixing procedure, i.e. the choice of Gribov copies [86][87][88] and discretisation artefacts [89]. Consequently, comparing the FRG IR band to the lattice propagators has to be taken with a grain of salt.…”

Reconstructing the gluon

“…Our discussion is based on the plethora of lattice results for decoupling gluon propagators at vanishing and finite temperature [53][54][55][56][57][58][59][60][61][62][63][64][65][66], for recent analytic fits to high precision data see, e.g., [67] and [68]. However, in our opinion the distinction between the different scenarios Section IV C 1, Section IV C 2 still requires a far higher precision.…”

Nonperturbative finite-temperature Yang-Mills theory

“…The lattice results are of the decoupling type, while our results are of the scaling type. Consequently, possible nonperturbative gauge fixing effects have to be kept in mind; see, e.g., [128][129][130][131]. This concerns in particular the ghost propagator, shown in Fig.…”