Exact Solution to the One-Plaquette Model of Induced QCD at Large $N$

TL;DR

This paper provides an exact large N solution to the one-plaquette induced QCD model, demonstrating its equivalence to standard QCD under certain conditions and discussing the continuum limit.

Contribution

It offers the first exact solution of the one-plaquette induced QCD model at large N using loop equations, establishing its equivalence to Wilson QCD.

Findings

Induced QCD matches Wilson QCD when inducing fields are sufficiently large.

The model is exactly solvable in the large N limit.

Discussion on the asymptotic freedom and continuum limit of induced QCD.

Abstract

The induced lattice gauge theory with various types of inducing fields in fundamental representation of $SU(N_{c})$ is considered. In a simple case of one-plaquette lattice the model is solved in the large $N_{c}$ limit by means of loop equations. Comparison with the solution of usual QCD shows the equivalence of induced and Wilson QCD providing that a mass and a number of flavours of inducing fields are sufficiently large. The possibility to take an asymptotically free continuum limit of induced QCD is discussed.