Difficulties in Inducing a Gauge Theory at Large N

TL;DR

The paper argues that the Kazakov-Migdal model at large N only involves zero area Wilson loops, effectively reducing the gauge action to a constant and causing gauge variables to drop out, challenging its viability as an induced gauge theory.

Contribution

It critically analyzes the Kazakov-Migdal model, revealing that at large N it only involves trivial Wilson loops, which limits its effectiveness as an induced gauge theory.

Findings

Only zero area Wilson loops are involved at large N.

The gauge action reduces to a constant, with gauge variables dropping out.

Plaquettes and non-trivial loops are effectively excluded.

Abstract

It is argued that the recently proposed Kazakov-Migdal model of induced gauge theory, at large $N$, involves only the zero area Wilson loops that are effectively trees in the gauge action induced by the scalars. This retains only a constant part of the gauge action excluding plaquettes or anything like them and the gauge variables drop out.