Two- and three-point functions in two-dimensional Landau-gauge Yang-Mills theory: Continuum results

TL;DR

This paper studies the Dyson-Schwinger equations for gluon and ghost propagators in two-dimensional Landau-gauge Yang-Mills theory, including a self-consistent ghost-gluon vertex and analyzing the infrared behavior of solutions.

Contribution

It introduces a self-consistent treatment of the ghost-gluon vertex in 2D and explores how the infrared exponent can vary with angle dependence and singularities.

Findings

Inclusion of ghost-gluon vertex self-consistently stabilizes solutions.

Evidence for the absence of decoupling solutions in 2D.

Infrared exponent can vary with angle dependence and singularities.

Abstract

We investigate the Dyson-Schwinger equations for the gluon and ghost propagators and the ghost-gluon vertex of Landau-gauge gluodynamics in two dimensions. While this simplifies some aspects of the calculations as compared to three and four dimensions, new complications arise due to a mixing of different momentum regimes. As a result, the solutions for the propagators are more sensitive to changes in the three-point functions and the ansaetze used for them at the leading order in a vertex a expansion. Here, we therefore go beyond this common truncation by including the ghost-gluon vertex self-consistently for the first time, while using a model for the three-gluon vertex which reproduces the known infrared asymptotics and the zeros at intermediate momenta as observed on the lattice. A separate computation of the three-gluon vertex from the results is used to confirm the stability of this behavior a posteriori. We also present further arguments for the absence of the decoupling solution in two dimensions. Finally, we show how in general the infrared exponent kappa of the scaling solutions in two, three and four dimensions can be changed by allowing an angle dependence and thus an essential singularity of the ghost-gluon vertex in the infrared.