The effects of Gribov copies in 2D gauge theories

Abstract In previous works, we have motivated 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 ≈ 0 . 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 discuss 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.