The effects of Gribov copies in 2D gauge theories

Abstract

In previous works, we have shown that the Gribov-Zwanziger action, which implements the restriction of the domain of integration in the path integral to the Gribov region, generates extra dynamical effects which influence the infrared behaviour of the gluon and ghost propagator in SU(N) Yang-Mills gauge theories. The latter are in good agreement with the most recent lattice data obtained at large volumes, both in 4D and in 3D. More precisely, the gluon propagator is suppressed and does not vanish at zero momentum, while the ghost propagator keeps a 1/p^2 behaviour for p^2\approx0. Instead, in 2D, the lattice data revealed a vanishing zero momentum gluon propagator and an infrared enhanced ghost, in support of the usual Gribov-Zwanziger scenario. We will now show that the 2D version of the Gribov-Zwanziger action still gives results in qualitative agreement with these lattice data, as the peculiar infrared nature of 2D gauge theories precludes the analogue of the dynamical effect otherwise present in 4D and 3D. Simultaneously, we also observe that the Gribov-Zwanziger restriction serves as an infrared regulating mechanism.

10 pages, 1 .eps figure

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Cited by in corpus (12)

• Gribov horizon and BRST symmetry: a few remarks
• Two- and three-point functions in two-dimensional Landau-gauge Yang-Mills theory: Continuum results
• Renormalizability of the Refined Gribov-Zwanziger action in the linear covariant gauges
• Study of the properties of the Gribov region in SU(N) Euclidean Yang-Mills theories in the maximal Abelian gauge
• On the gauge-algebra dependence of Landau-gauge Yang-Mills propagators
• Dimension two condensates in the Gribov-Zwanziger theory in the Coulomb gauge
• Remarks on the effects of the Gribov copies on the infrared behavior of higher dimensional Yang-Mills theory
• The analytic structure of three-point functions from contour deformations
• Refined Gribov-Zwanziger theory coupled to scalar fields in the Landau gauge
• Exploring new horizons of the Gribov problem in Yang-Mills theories
• Functional renormalization of QCD in $1+1$ dimensions: four-fermion interactions from quark-gluon dynamics
• Color-octet nonrelativistic QCD matrix elements for heavy quarkonium decays in the refined Gribov-Zwanziger theory