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This talk offers a brief review of the determination of coupling constants in the framework of dimensionally reduced effective field theories for thermal QCD, specializing on its gluonic sector. Interestingly, higher-order operators that go beyond the usual super-renormalizable truncation of the effective theory need to be considered when matching parameters at three loops.
We analyze 3-loop contributions to the gauge coupling felt by ultrasoft (magnetostatic) modes in hot Yang-Mills theory. So-called soft/hard terms, originating from dimension-six operators within the soft effective theory, are shown to cancel 1097/109
Perturbation theory for non-Abelian gauge theories at finite temperature is plagued by infrared divergences caused by magnetic soft modes $sim g^2T$, which correspond to the fields of a 3d Yang-Mills theory. We revisit a gauge invariant resummation s
A detailed description of the method for analytical evaluation of the three-loop contributions to renormalization group functions is presented. This method is employed to calculate the charge renormalization function and anomalous dimensions for non-
We revisit the renormalisation group equations (RGE) for general renormalisable gauge theories at one- and two-loop accuracy. We identify and correct various mistakes in the literature for the $beta$-functions of the dimensionful Lagrangian parameter
We extend a constrained version of Implicit Regularization (CIR) beyond one loop order for gauge field theories. In this framework, the ultraviolet content of the model is displayed in terms of momentum loop integrals order by order in perturbation t