Wilson loops in unitary matrix models at finite $N$

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.

arXiv comment38 pages

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• Unitary matrix models and random partitions: Universality and multi-criticality
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• Non-Perturbative Large N Trans-series for the Gross-Witten-Wadia Beta Function
• Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories
• Phases of unitary matrix models and lattice QCD2
• Large $N$ expansion of Wilson loops in the Gross-Witten-Wadia matrix model
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• Finite $N$ unitary matrix model
• Asymptotics of the partition function of the perturbed Gross-Witten-Wadia unitary matrix model
• The Phases of Chaos