HIERARCHY OF EFFECTIVE-FIELD THEORIES OF HOT ELECTROWEAK MATTER

A hierarchy of effective three-dimensional theories of finite temperature electroweak matter is studied. First an integration over nonstatic modes leads to an effective theory containing a gauge field A(i)a, an adjoint Higgs field A0a, and the fundamental Higgs field phi(a). We carry out the integration in the one-loop approximation, study renormalization effects, and estimate quantitatively those terms of the effective action which are suppressed by inverse powers of the temperature. Second, because of the existence of well-separated thermal mass scales, A0a can be integrated over, and finally also phi(a), leaving an effective theory of the A(i)a. In the analysis of the subsequent models particular attention is paid to the screening of the magnetic fluctuations due to the integrated-out degrees of freedom.