Abstract
We compute correlation functions of three-dimensional Landau-gauge Yang-Mills theory with the Functional Renormalisation Group. Starting from the classical action as only input, we calculate the non-perturbative ghost and gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon, and four-gluon vertices in a comprehensive truncation scheme. Compared to the physical case of four spacetime dimensions, we need more sophisticated truncations due to significant contributions from non-classical tensor structures. In particular, we apply a special technique to compute the tadpole diagrams of the propagator equations, which captures also all perturbative two-loop effects, and compare our correlators with lattice and Dyson-Schwinger results.
Highlights
Functional methods such as the Functional Renormalisation Group (FRG) or Dyson-Schwinger equations (DSEs) are non-perturbative first-principles approaches to Quantum Chromodynamics (QCD), and they are complementary to lattice simulations
The paper is organized as follows: In Sec.2 we review the treatment of YM theory with the FRG using a vertex expansion for the effective action
After discussing the truncation dependence of our results we provide an extensive comparison to results from lattice gauge theory and Dyson-Schwinger equations
Summary
Functional methods such as the Functional Renormalisation Group (FRG) or Dyson-Schwinger equations (DSEs) are non-perturbative first-principles approaches to Quantum Chromodynamics (QCD), and they are complementary to lattice simulations. At finite density the latter approach is hampered by a sign problem, while the former approaches face convergence and accuracy problems. The most advanced results for YM theory in three dimensions within functional approaches have been obtained in a recent DSE investigation [31]. The present work builds on these advances, with a focus on the effects of including non-classical vertices and tensor structures in the tadpole diagrams of the gluon and ghost propagator equations. We check the independence of the regulator and describe the computational setup in the appendices
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