Lower dimensional Yang-Mills theory as a laboratory to study the infrared regime

TL;DR

This paper demonstrates that lower-dimensional Yang-Mills theories can effectively serve as simplified models to study the complex infrared behavior of gauge theories, facilitating easier lattice simulations across different dimensions.

Contribution

It introduces a power counting scheme showing the qualitative and quantitative similarity of infrared behavior in 2, 3, and 4 dimensions, enabling simplified lattice studies.

Findings

Infrared Greens functions are similar across dimensions.

Lower dimensions provide a practical testing ground for gauge theory approximations.

Lattice simulations in lower dimensions can inform higher-dimensional theories.

Abstract

Lattice studies of the infrared regime of gauge theories are complicated by the required extensive limits, the performed gauge fixing and the demand for high statistics. Using a general power counting scheme for the infrared limit of Landau gauge SU(N) Yang-Mills theory in arbitrary dimensions we show that the infrared behavior of Greens functions is both qualitatively and quantitatively similar in two, three and four spacetime dimensions. Therefore, lower dimensional lattice simulations can serve as a simplified laboratory to analyze the presently applied approximations and to obtain first results for higher correlation functions.