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

Abstract

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. Alternative elimination of the pion and sigma propagators provides the renormalized NLO effective potential for the expectation values of the N-vector and of the auxiliary field with the same accuracy.

RevTeX4, 19 pages, 3 figures. Version published Phys. Rev. D

References in corpus (10)

• Nonperturbative renormalization for 2PI effective action techniques
• Gapless Hartree-Fock Resummation Scheme for the O(N) Model
• Linear sigma model at finite density in the 1/N expansion to next-to-leading order
• Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of $\lambda {\varphi }^4$ field theory
• Renormalisability of the 2PI-Hartree approximation of multicomponent scalar models in the broken symmetry phase
• Renormalized broken-symmetry Schwinger-Dyson equations and the 2PI-1/N expansion for the O(N) model
• Thermodynamics of O(N) sigma models: 1/N corrections
• Counterterm resummation for 2PI-approximation in constant background
• Renormalization of O(N) model in 1/N expansion in auxiliary field formalism
• Phantom field fluctuation induced Higgs effect

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• Study of chiral symmetry restoration in linear and nonlinear O(N) models using the auxiliary field method
• Resummations in the Bloch-Nordsieck model
• A critical look at the role of the bare parameters in the renormalization of Phi-derivable approximations
• Arithmetical rank of lexsegment edge ideals
• Broken symmetry phase solution of the phi^4 model at two-loop level of the Phi-derivable approximation
• Thermodynamics of the O(3) model in 1+1 dimensions: lattice vs. analytical results
• Revisiting $O(N)$ $\sigma$ model at unphysical pion masses and high temperatures. II. The vacuum structure and thermal $\sigma$ pole trajectory with cross-channel improvements
• Renormalization of the 2PI-Hartree approximation in a broken phase with nonzero superflow
• Renormalized O(N) model at next-to-leading order of the 1/N expansion: Effects of the Landau pole
• Invariants of some classes of monomial ideals