Multiple phases in a generalized Gross-Witten-Wadia matrix model

Abstract

We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large $N$ results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large $N$ (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

22 pages

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Cited by in corpus (7)

• Multiple phases and meromorphic deformations of unitary matrix models
• Deformed Cauchy random matrix ensembles and large $N$ phase transitions
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• Generalised unitary group integrals of Ingham-Siegel and Fisher-Hartwig type
• 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
• Fermionic Matrix Models and Bosonization