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

2020/07/16 by Jorge G. Russo, Miguel Tierz
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Geology #Materials science #Mathematics #Matrix (chemical analysis) #Random Matrices and Applications #hep-th #math-ph #math.MP

paper · pdf · doi:10.1007/jhep09(2020)081

published as J. High Energ. Phys. 2020, 81 (2020) · 22 pages

arxiv created 2020/07/16 · openalex publication_date 2020/09/01 · arxiv updated 2020/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A bstract 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.

Citations

• A Study of U(N) Lattice Gauge Theory in 2-dimensions
• On the distribution of the length of the longest increasing subsequence of random permutations
• On the distributions of the lengths of the longest monotone subsequences in random words
• N = ∞ phase transition in a class of exactly soluble model lattice gauge theories