Flows and solitary waves in unitary matrix models with logarithmic potentials

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.

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Complex Langevin dynamics in large N unitary matrix models

Physical Review D ◽

10.1103/physrevd.98.034501 ◽

2018 ◽

Vol 98 (3) ◽

Cited By ~ 5

Author(s):

Pallab Basu ◽

Kasi Jaswin ◽

Anosh Joseph

Keyword(s):

Matrix Models ◽

Langevin Dynamics ◽

Unitary Matrix ◽

Large N

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AN OPERATOR FORMALISM FOR UNITARY MATRIX MODELS

Modern Physics Letters A ◽

10.1142/s0217732391003183 ◽

1991 ◽

Vol 06 (29) ◽

pp. 2727-2739 ◽

Cited By ~ 1

Author(s):

K. N. ANAGNOSTOPOULOS ◽

M. J. BOWICK ◽

N. ISHIBASHI

Keyword(s):

Orthogonal Polynomials ◽

Matrix Models ◽

Pseudodifferential Operators ◽

Scaling Limit ◽

Unitary Matrix ◽

String Equation ◽

Operator Formalism ◽

Multicritical Point ◽

Compact Formulation ◽

Double Scaling Limit

We analyze the double scaling limit of unitary matrix models in terms of trigonometric orthogonal polynomials on the circle. In particular we find a compact formulation of the string equation at the kth multicritical point in terms of pseudodifferential operators and a corresponding action principle. We also relate this approach to the mKdV hierarchy which appears in the analysis in terms of conventional orthogonal polynomials on the circle.

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Black hole/string transition for the small Schwarzschild black hole of AdS 5 × S5 and critical unitary matrix models

The European Physical Journal C ◽

10.1140/epjc/s10052-006-0049-x ◽

2006 ◽

Vol 48 (2) ◽

pp. 647-665 ◽

Cited By ~ 42

Author(s):

L. Álvarez-Gaumé ◽

P. Basu ◽

M. Mariño ◽

S.R. Wadia

Keyword(s):

Black Hole ◽

Matrix Models ◽

Unitary Matrix ◽

Schwarzschild Black Hole

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Reduced unitary matrix models and the hierarchy of τ-functions

Nuclear Physics B ◽

10.1016/0550-3213(91)90365-5 ◽

1991 ◽

Vol 354 (2-3) ◽

pp. 496-530 ◽

Cited By ~ 24

Author(s):

Mark J. Bowick ◽

Aleksey Morozov ◽

Daniel Shevitz

Keyword(s):

Matrix Models ◽

Unitary Matrix

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UNITARY MATRIX MODELS AND 2D QUANTUM GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732392002226 ◽

1992 ◽

Vol 07 (29) ◽

pp. 2753-2762 ◽

Cited By ~ 28

Author(s):

S. DALLEY ◽

C. V. JOHNSON ◽

T. R. MORRIS ◽

A. WÄTTERSTAM

Keyword(s):

Matrix Models ◽

Integrable Hierarchies ◽

Renormalization Group Equation ◽

Closed String ◽

Singular Solutions ◽

Unitary Matrix ◽

Group Equation ◽

Gravitational System ◽

Large N ◽

Matrix Integrals

The KdV and modified KdV integrable hierarchies are shown to be different descriptions of the same 2D gravitational system — open-closed string theory. Non-perturbative solutions of the multicritical unitary matrix models map to non-singular solutions of the 'renormalization group' equation for the string susceptibility, [Formula: see text]. We also demonstrate that the large-N solutions of unitary matrix integrals in external fields, studied by Gross and Newman, equal the non-singular pure closed-string solutions of [Formula: see text].

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Unitary integrals and related matrix models

10.1093/oxfordhb/9780198744191.013.17 ◽

2018 ◽

Author(s):

Nicolas Orantin

Keyword(s):

Matrix Models ◽

Unitary Matrix ◽

Technical Tool ◽

Basic Properties ◽

Matrix Integrals ◽

Unitary Model ◽

M Theory ◽

Pair Correlator

This article examines the basic properties of unitary matrix integrals using three matrix models: the ordinary unitary model, the Brézin-Gross-Witten (BGW) model and the Harish-Chandra-Itzykson-Zuber (HCIZ) model. The tricky sides of the story are given special attention, such as the de Wit-’t Hooft anomaly in unitary integrals and the problem of correlators with Itzykson-Zuber measure. The method of character expansions is also emphasized as a technical tool. The article first provides an overview of the theory of the BGW model, taking into account the de Wit-’t Hooft anomaly and the M-theory of matrix models, before discussing the theory of the HCIZ integral. In particular, it describes the basics of character calculus, character expansion of the HCIZ integral, character expansion for the BGW model and Leutwyler-Smilga integral, and pair correlator in HCIZ theory.

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