Some Remarks About Induced QCD

TL;DR

This paper explores the possibility of inducing QCD from lattice models with scalar fields in the adjoint representation at infinite coupling, providing exact solutions and connecting to continuum matrix models.

Contribution

It presents an exact saddlepoint solution for the large N limit with a quadratic scalar potential and links lattice QCD models to continuum matrix models.

Findings

Derived an exact saddlepoint solution for the theory at infinite N.

Showed how the continuum D=1 matrix model can be obtained from the lattice approach.

Discussed implications for understanding induced QCD models.

Abstract

Migdal and Kazakov have suggested that lattice QCD with an adjoint representation scalar in the infinite coupling limit could induce QCD. I find an exact saddlepoint of this theory for infinite $N$ in the case of a quadratic scalar potential. I discuss some aspects of this solution and also show how the continuum D=1 matrix model with an arbitrary potential can be reproduced through this approach.