Mixed Model of Induced QCD

TL;DR

This paper investigates the induced QCD model, addressing Z_N symmetry breaking issues, and proposes a solution involving heavy fermions, resulting in an exactly solvable model with novel vacuum regimes and symmetry conditions.

Contribution

It introduces a mixed model of induced QCD with heavy fermions that preserves solvability and explores new vacuum structures and symmetry breaking conditions.

Findings

No Z_N symmetry breaking in strong coupling phase for arbitrary potential.

A new regime with two vacuum densities emerges at large N_f/N ratios.

Symmetry breaking depends on eigenvalue conditions and potential adjustments.

Abstract

The problems with the $Z_N$ symmetry breaking in the induced QCD are analyzed. We compute the Wilson loops in the strong coupling phase, but we do not find the $Z_N$ symmetry breaking, for arbitrary potential. We suggest to bypass this problem by adding to the model a heavy fermion field in a fundamental representation of $ SU(N) $. Remarkably, the model still can be solved exactly by the Rieman-Hilbert method, for arbitrary number $N_f$ of flavors. At $ N_f \ll N \rightarrow \infty $ there is a new regime, with two vacuum densities. The $Z_N$ symmetry breaking density satisfies the linear integral equation, with the kernel, depending upon the old density. The symmetry breaking requires certain eigenvalue condition, which takes some extra parameter adjustment of the scalar potential.