Journal of High Energy Physics

, 2012:35

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


DOI: 10.1007/JHEP11(2012)035

Cite this article as:
Huber, M.Q., Maas, A. & von Smekal, L. J. High Energ. Phys. (2012) 2012: 35. doi:10.1007/JHEP11(2012)035


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 ansätze used for them at the leading order in a vertex 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 κ 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.


Confinement QCD Field Theories in Lower Dimensions Nonperturbative Effects 

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Markus Q. Huber
    • 1
  • Axel Maas
    • 2
  • Lorenz von Smekal
    • 1
  1. 1.Institut für KernphysikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Institute for Theoretical PhysicsFriedrich-Schiller-University JenaJenaGermany

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