SU(5)+Adjoint Higgs Model at Finite Temperature

A three-dimensional effective theory of the finite-temperature SU(5)+adjoint Higgs model is constructed using the method of dimensional reduction. The resulting theory can be used for computer simulations of the GUT phase transition of the early universe. In this paper the transition is analyzed at two-loop level in perturbation theory. The structure of the effective theory does not essentially depend on the matter contents of the original four-dimensional one. Therefore the analysis of this paper applies also to more realistic theories.