Spontaneously broken ground states of the U(n)_L x U(n)_R linear sigma model at large n

TL;DR

This paper analyzes the symmetry breaking patterns in the U(n)_L x U(n)_R linear sigma model at large n, revealing metastable states and their stability under external fields, using a 1/n expansion approach.

Contribution

It introduces a novel formulation with auxiliary fields to study symmetry breaking in the meson model at large n, identifying metastable minima and their behavior under external influences.

Findings

Existence of metastable minima with additional symmetry breaking

External fields can convert metastable states into true ground states

Effective potential constructed at leading order in 1/n expansion

Abstract

Symmetry breaking patterns of the U(n)_L x U(n)_R symmetric meson model are investigated in a formulation involving three auxiliary composite fields. The effective potential is constructed at leading order in the 1/n expansion for a condensate belonging to the center of the U(n) group. A wide region is found in the coupling space where in addition to the condensate proportional to the unit matrix, also metastable minima exist, in which a further breakdown of the diagonal U_V(n) symmetry to U_V(n-1) is realized. Application of a moderate external field conjugate to this component of the order parameter changes this state into the true ground state of the system.