Possible large-N transitions for complex Wilson loop matrices

TL;DR

This paper introduces a simple complex matrix model that generalizes large-N phase transitions observed in unitary matrices, revealing a potential phase transition in complex Wilson loop matrices in field theories with a planar limit.

Contribution

It proposes a new complex matrix model that captures large-N phase transitions, extending known results from unitary matrices to complex cases.

Findings

Identifies a phase transition point where smoothness breaks down.

Shows a perturbative to non-perturbative regime change.

Suggests similar phase behavior in complex Wilson loop matrices.

Abstract

It is shown that a very simple multiplicative random complex matrix model generalizes the large-N phase structure found in the unitary case: A perturbative regime is joined to a non-perturbative regime at a point where the smoothness of some quantities breaks down. A generic complex Wilson loop matrix in a field theory admitting a 't Hooft planar limit could display a phase transition in that limit as nonlinear effects become dominating over linear ones.