Ghost dissection

TL;DR

This paper proves that in two-dimensional Yang-Mills theories, a positive ghost propagator requires a zero-momentum gluon propagator, aligning with lattice data and contrasting higher dimensions.

Contribution

It establishes a necessary condition linking ghost and gluon propagators in 2D Yang-Mills theories using Dyson-Schwinger equations.

Findings

Positive ghost propagator in 2D requires zero-momentum gluon propagator.

Decoupling gluon solutions are forbidden in 2D, unlike in 3D and 4D.

Results align with lattice simulations.

Abstract

We show that a necessary condition to have a positive Landau-gauge ghost propagator in d=2 Yang-Mills theories is a vanishing zero-momentum gluon propagator. Our proof is based on a careful scrutinizing of the ghost Dyson-Schwinger equation. Said otherwise, the Gribov no-pole condition forbids the occurrence of the "decoupling/massive" gluon propagator solution in d=2, in sharp contrast with d=3 and 4, but consistent with state-of-the-art lattice data.