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A fully explicit renormalized quantum action functional is constructed forthe O(N)-model in the auxiliary field formulation at next-to-leading order(NLO) of the 1/N expansion. Counterterms are consistently and explicitlyderived for arbitrary constant vacuum expectation value of the scalar andauxiliary fields. The renormalized NLO pion propagator is exact at this orderand satisfies Goldstone's theorem. Elimination of the auxiliary field sector atthe level of the functional provides with order N^0 accuracy the renormalizedeffective action of the model in terms of the original variables. Alternativeelimination of the pion and sigma propagators provides the renormalized NLOeffective potential for the expectation values of the N-vector and of theauxiliary field with the same accuracy.

Renormalized effective actions for the O(N) model at next-to-leading order of the 1/N expansion