Renormalization of O(N) model in 1/N expansion in auxiliary field formalism

TL;DR

This paper investigates the renormalization process of the O(N) model using auxiliary field formalism within the 1/N expansion at finite temperature, providing a general strategy and explicit calculations up to next-to-leading order.

Contribution

It introduces a comprehensive renormalization approach for the O(N) model in auxiliary field formalism, applicable at arbitrary order and finite temperature, including explicit next-to-leading order calculations.

Findings

Renormalization is feasible for all condensate values.

Counterterms are temperature independent.

First nontrivial counterterms depend on the cutoff.

Abstract

We study the renormalization of the O(N) model using the auxiliary field formalism (Hubbard-Stratonovich transformation) in the 1/N expansion at finite temperature. We provide the general strategy of renormalization for arbitrary order, and make calculation up to next-to-leading order. We show that renormalization is possible for any values of the condensates, prove the temperature independence of the counterterms and determine the cutoff dependence of the first nontrivial counterterm parts.