One-loop dimensional reduction of the linear (sigma) model (English)

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We perform the dimensional reduction of the linear (sigma) model at one- loop level. The effective of the reduced theory obtained from the integration over the nonzero Matsubara frequencies is exhibited. Thermal mass and coupling constant renormalization constants are given, as well as the thermal renormalization group which controls the dependence of the counterterms on the temperature. We also recover, for the reduced theory, the vacuum instability of the model for large N. (author) 28 refs.