Generic rules for high temperature dimensional reduction and their application to the Standard Model

We formulate the rules for dimensional reduction of a generic finite temperature gauge theory to a simpler three-dimensional effective bosonic theory in terms of a matching of Green functions in the full and the effective theory, and present a computation of a generic set of 1- and 2-loop graphs needed for the application of these rules. As a concrete application we determine the explicit mapping of the physical parameters of the standard electroweak theory to a three-dimensional SU(2) x U(1) gauge-Higgs theory. We argue that this three-dimensional theory has a universal character and appears as an effective theory for many extensions of the Standard Model.