Bose Condensation and $Z_N$ Symmetry Breaking in the Mixed Model of Induced QCD

TL;DR

This paper analyzes a large N induced QCD model with heavy fermions, revealing spontaneous Z_N symmetry breaking, Bose condensation of scalar eigenvalues, and a new local limit that could facilitate realistic QCD induction.

Contribution

It demonstrates spontaneous Z_N symmetry breaking and Bose condensation in a large N induced QCD model, introducing a novel local limit with potential for realistic QCD induction.

Findings

Z_N symmetry is spontaneously broken at large N.

A Bose condensate of scalar eigenvalues is formed.

A new local limit with a vanishing mass scale is identified.

Abstract

The mixed model of the large $ N $ induced QCD, with $ N_f \ll N $ flavors of heavy fermions in fundamental representation, is solved in the local limit. The $ Z_N$ symmetry is broken spontaneously in the large $ N $ limit, evading the Elitzur "no-go" theorem. As a result of this symmetry breaking, there is the Bose condensate of the eigenvalues of the scalar field, proportional to $ \frac{N_f}{N} $. This condensate leads to the mass unit, which goes to zero as fractional power of $ \frac{N_f}{N} $, thus defining the new kind of the local limit of this lattice theory. There is a strong coupling region below this mass scale, which revives the hopes of induction of realistic QCD.