A Simple Model Inducing QCD

TL;DR

This paper introduces a simplified lattice gauge model with a fundamental scalar field, analyzing its large N limit and phase transitions, providing new insights into gauge theories without extra symmetries.

Contribution

The paper presents a novel lattice model inducing gauge theory with only linear scalar-gauge interactions, avoiding extra U(1) symmetries, and analyzes its large N behavior and phase structure.

Findings

Model exhibits phase transitions at specific coupling points.

Large N limit yields an effective eigenvalue interaction theory.

Use of orthogonal polynomials leads to nonlinear equations describing the model.

Abstract

A simple lattice model inducing a gauge theory is considered. The model describes an interaction of a gauge field to an $N\times N$ complex matrix scalar field transforming as a field in the fundamental representation. In contrast to the Kazakov-Migdal model the model contains only the linear interaction between scalar and gauge lattice fields. This model does not suffer from extra local U(1) symmetries. In an approximation of a translation invariant master field the large N limit of the model is investigated. At large N the gauge fields can be integrated out yielding an effective theory describing an interaction of eigenvalues of the master field. The reduced model exhibits phase transitions at the points $\beta_{\bar {cr}}$ and $\beta _{\underline{cr}}$ and the region $(\beta_{\bar{cr}}, \beta_{\underline{cr}})$ separates the strong and weak regions of the model. To study the behaviour of the model at large $N$ in more systematic way the quenched momentum prescription with constraints for treating the large N limit of gauge theories is used. With the help of the technique of orthogonal polynomials nonlinear equations describing the large N limit of the reduced model {\it with quenching} are presented.