SU($N$) Cartan-Weyl bases and color factors

TL;DR

This paper explores the use of Cartan-Weyl bases for evaluating SU(N) color factors in non-abelian gauge theories at finite temperature, highlighting advantages over Cartesian bases.

Contribution

It extends previous work by detailing the evaluation of SU(N) color factors within Cartan-Weyl bases, improving the understanding of gauge theories with constant temporal backgrounds.

Findings

Enhanced methods for calculating SU(N) color factors

Better handling of confinement/deconfinement transitions

Clarification of Cartan-Weyl basis advantages

Abstract

Constant temporal backgrounds have become a convenient tool for the discussion of continuum non-abelian gauge theories at finite temperature, as they provide a grasp on the confinement/deconfinement transition. It has been pointed that such backgrounds are better dealt with within so-called Cartan-Weyl color bases, rather than within the standard Cartesian bases. Here, we discuss the specificities of the evaluation of SU($N$) color factors within these bases, extending the discussion in Ref. [1].