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

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