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

TL;DR

This paper investigates a generalized Gross-Witten-Wadia matrix model with characteristic polynomial insertions, revealing a complex phase structure in the large N limit through exact formulas and asymptotic analysis.

Contribution

It introduces a new matrix model interpolating between solvable models and provides exact formulas and phase analysis in the large N limit.

Findings

Exact formulas for partition functions and Wilson loops.

Identification of a rich phase structure in the model.

Application of Szeg"o theorem with Fisher-Hartwig singularity.

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 Szeg\"o 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.