Symmetry Nonrestoration in a Resummed Renormalized Theory at High Temperature

We reinvestigate the interesting phenomenon of symmetry nonrestoration at high temperature in the multifield O(N_1) X O(N_2) model. We apply modified self-consistent resummation (MSCR) in order to obtain the scalar dressed masses and find in what circumstances a resummed multifield theory which has symmetry (non)restoration can be renormalized. It is shown that, aside from the consistency of the MSCR method, the basic ingredient that guarantees the renormalization of a multifield model within a resummation approach is the T^2 mass behavior of field theory at high temperature.