A renormalized large-n solution of the U(n) x U(n) linear sigma model in the broken symmetry phase

TL;DR

This paper develops a large-n analytical solution for the U(n) x U(n) linear sigma model in the broken symmetry phase, utilizing Dyson-Schwinger equations and renormalization techniques.

Contribution

It introduces a renormalized large-n solution of the U(n) x U(n) sigma model with auxiliary fields, under assumptions about mass hierarchies, and demonstrates its renormalizability.

Findings

Constructed a large-n solution within the bare vertex approximation.

Explicitly demonstrated the renormalizability through counterterm construction.

Analyzed the symmetry-breaking phase of the sigma model.

Abstract

Dyson-Schwinger equations for the U(n) x U(n) symmetric matrix sigma model reformulated with two auxiliary fields in a background breaking the symmetry to U(n) are studied in the so-called bare vertex approximation. A large n solution is constructed under the supplementary assumption so that the scalar components are much heavier than the pseudoscalars. The renormalizability of the solution is investigated by explicit construction of the counterterms.