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

Understand

A fully explicit renormalized quantum action functional is constructed for the O(N)-model in the auxiliary field formulation at next-to-leading order (NLO) of the 1/N expansion.

• Counterterms are consistently and explicitly derived for arbitrary constant vacuum expectation value of the scalar and auxiliary fields.
• The renormalized NLO pion propagator is exact at this order and satisfies Goldstone's theorem.
• Elimination of the auxiliary field sector at the level of the functional provides with order N^0 accuracy the renormalized effective action of the model in terms of the original variables.