Ghost dissection

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. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.