The effects of Gribov copies in 2D gauge theories

TL;DR

This paper investigates the impact of Gribov copies on 2D gauge theories, showing that the Gribov-Zwanziger approach qualitatively aligns with lattice data and acts as an infrared regulator.

Contribution

It demonstrates that the 2D Gribov-Zwanziger action reproduces key infrared features of lattice data and functions as an effective infrared regulator.

Findings

2D Gribov-Zwanziger action aligns qualitatively with lattice data

The restriction acts as an infrared regulator in 2D

Infrared behavior differs from 3D and 4D cases

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.