Nonperturbative properties of Yang-Mills theories

TL;DR

This paper reviews recent nonperturbative studies of Yang-Mills correlation functions across various gauges and dimensions, highlighting the role of truncations, resummation, and gauge choices in understanding gauge theories.

Contribution

It provides a comprehensive overview of correlation functions in different gauges and dimensions, emphasizing the impact of truncations and resummation techniques in nonperturbative analyses.

Findings

Correlation functions in Landau gauge obtained from equations of motion.

Effects of truncations studied in 2D and 3D cases.

Resummation in Dyson-Schwinger equations explained for 4D.

Abstract

Yang-Mills theories are an important building block of the standard model and in particular of quantum chromodynamics. Its correlation functions describe the behavior of its elementary particles, the gauge bosons. In quantum chromodynamics, the correlation functions of the gluons are basic ingredients for calculations of hadrons from bound state equations or properties of its phase diagram with functional methods. Correlation functions of gluons are defined only in a gauge fixed setting. The focus of many studies is the Landau gauge which has some features that alleviate calculations. I discuss recent results of correlation functions in this gauge obtained from their equations of motions. Besides the four-dimensional case also two and three dimensions are treated, since the effects of truncations, viz., the procedure to render the infinitely large system of equations finite, can be studied more directly in these cases. In four dimensions, the anomalous running of dressing functions plays a special role and it is explained how resummation is realized in the case of Dyson-Schwinger equations. Beyond the Landau gauge other gauges can provide additional insights or can alleviate the development of new methods. Some aspects or ideas are more easily accessible in alternative gauges and the results presented here for linear covariant gauges, the Coulomb gauge and the maximally Abelian gauge help to refine our understanding of Yang-Mills theories.