# Wilson loops in unitary matrix models at finite $N$

## TL;DR

This paper analyzes Wilson loops in the GWW unitary matrix model at finite N, exploring perturbative and non-perturbative corrections, proposing a large N master field, and examining large representations and phase transitions.

## Contribution

It provides exact finite N results for Wilson loops, introduces a large N master field with a unique eigenvalue distribution, and studies phase transitions in the model.

## Key findings

- Exact finite N Wilson loop calculations for arbitrary representations
- Proposal of a large N master field with distinctive eigenvalue distribution
- Analysis of phase transitions related to Hagedorn/deconfinement phenomena

## Abstract

It is known that the expectation value of Wilson loops in the Gross-Witten-Wadia (GWW) unitary matrix model can be computed exactly at finite $N$ for arbitrary representations. We study the perturbative and non-perturbative corrections of Wilson loops in the $1/N$ expansion, either analytically or numerically using the exact result at finite $N$. As a by-product of the exact result of Wilson loops, we propose a large $N$ master field of GWW model. This master field has an interesting eigenvalue distribution. We also study the Wilson loops in large representations, called Giant Wilson loops, and comment on the Hagedorn/deconfinement transition of a unitary matrix model with a double trace interaction.