# Two- and three-point Green's functions in two-dimensional Landau-gauge Yang-Mills theory

## TL;DR

This study investigates two-dimensional SU(2) Yang-Mills theory's Green's functions in Landau gauge using lattice simulations, confirming theoretical predictions and analyzing finite volume effects with large lattices.

## Contribution

It provides the first comprehensive lattice analysis of two- and three-point Green's functions in 2D Yang-Mills theory, confirming infrared exponents and behavior predicted by continuum approaches.

## Key findings

- Green's functions behave similarly to higher dimensions
- Finite volume effects are systematically characterized
- Infrared exponents match Dyson-Schwinger and stochastic quantization results

## Abstract

The ghost and gluon propagator and the ghost-gluon and three-gluon vertex of two-dimensional SU(2) Yang-Mills theory in (minimal) Landau gauge are studied using lattice gauge theory. It is found that the results are qualitatively similar to the ones in three and four dimensions. The propagators and the Faddeev-Popov operator behave as expected from the Gribov-Zwanziger scenario. In addition, finite volume effects affecting these Green's functions are investigated systematically. The critical infrared exponents of the propagators, as proposed in calculations using stochastic quantization and Dyson-Schwinger equations, are confirmed quantitatively. For this purpose lattices of volume up to (42.7 fm)^2 have been used.