Correlation functions of three-dimensional Yang-Mills theory from the FRG

TL;DR

This paper uses the Functional Renormalisation Group to compute non-perturbative correlation functions in three-dimensional Yang-Mills theory, providing detailed propagators and vertices and comparing them with lattice and Dyson-Schwinger results.

Contribution

It introduces a comprehensive truncation scheme for three-dimensional Yang-Mills theory using FRG, including a novel technique for tadpole diagrams that captures two-loop effects.

Findings

Agreement with lattice and Dyson-Schwinger results

Detailed momentum-dependent propagators and vertices

Enhanced truncation scheme for non-perturbative effects

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.