Real-time non-Abelian gauge coupling at finite temperature: Temperature and vertex-configuration dependences

A one-loop analysis of the non-Abelian effective gauge couplings at finite temperature is carried out in the real-time formalism of thermal field theory, mainly focusing on the problem of the strong vertex-configuration dependence of the effective charge. The important observations are as follows: (i) Depending on the vertex configuration the coupling changes drastically, even its screening property as well as its leading temperature behavior; (ii) the leading large-$T$ behavior of the real-time thermal coupling is controlled by the contribution from the infrared region of loop momenta; (iii) the marked difference between couplings defined in the magnetic and electric prescriptions is clarified. The relation between couplings defined in the real-time versus imaginary-time formalism is also discussed.