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.

38 pages

References in corpus (7)

• Holographic Wilson Loops
• Wilson Loops of Anti-symmetric Representation and D5-branes
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• Multiply wound Polyakov loops at strong coupling
• Fine structure of Hagedorn transitions
• Complex saddles in the Gross-Witten-Wadia matrix model
• Comments on k-Strings at Large N

Cited by in corpus (14)

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• Large $N$ expansion of Wilson loops in the Gross-Witten-Wadia matrix model
• Charge fluctuation entropy of Hawking radiation: a replica-free way to find large entropy
• A Scaling Relation, $Z_m$-type Deconfinement Phases and Imaginary Chemical Potentials in Finite Temperature Large-$N$ Gauge Theories
• Complex Langevin Method on Rotating Matrix Quantum Mechanics at Thermal Equilibrium
• Construction of irregular conformal/W block and flavor mass relations of $\mathcal{N}=2$ SUSY gauge theory from the $A_{n-1}$ quiver matrix model
• Matrix models and non-Abelian T dual of $Ad{S}_5\times S^5$
• Finite $N$ unitary matrix model
• The Phases of Chaos
• Asymptotics of the partition function of the perturbed Gross-Witten-Wadia unitary matrix model