scholarly journals Duality and replicas for a unitary matrix model

2010 ◽  
Vol 2010 (7) ◽  
Author(s):  
E. Brézin ◽  
S. Hikami
Keyword(s):  
Matrix Model ◽  
Unitary Matrix

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

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Jorge G. Russo ◽  
Miguel Tierz
Keyword(s):  
Partition Function ◽  
Matrix Models ◽  
Characteristic Polynomial ◽  
Matrix Model ◽  
Phase Structure ◽  
Unitary Matrix ◽  
Two Dimensional ◽  
Toeplitz Determinants ◽  
Dimensional Parameter ◽  
Planar Limit

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.

scholarly journals Emergent phase space description of unitary matrix model

2017 ◽  
Vol 2017 (11) ◽  
Author(s):  
Arghya Chattopadhyay ◽  
Parikshit Dutta ◽  
Suvankar Dutta
Keyword(s):  
Phase Space ◽  
Matrix Model ◽  
Unitary Matrix ◽  
Space Description

High-gradient operators of the unitary matrix-model

1990 ◽  
Vol 81 (1) ◽  
pp. 95-97 ◽  
Author(s):  
Igor V. Lerner ◽  
Franz Wegner
Keyword(s):  
Matrix Model ◽  
Unitary Matrix ◽  
High Gradient

EXCITATIONS AND INTERACTIONS IN d=1 STRING THEORY

1991 ◽  
Vol 06 (11) ◽  
pp. 1961-1984 ◽  
Author(s):  
ANIRVAN M. SENGUPTA ◽  
SPENTA R. WADIA
Keyword(s):  
Matrix Model ◽  
Periodic Wave ◽  
Density Fluctuations ◽  
Dirac Fermion ◽  
Unitary Matrix ◽  
Additional Parameter ◽  
Continuum Approach ◽  
The Matrix ◽  
The One ◽  
The Continuum

We discuss the singlet sector of the d=1 matrix model in terms of a Dirac fermion formalism. The leading order two- and three-point functions of the density fluctuations are obtained by this method. This allows us to construct the effective action to that order and hence provide the equation of motion. This equation is compared with the one obtained from the continuum approach. We also compare continuum results for correlation functions with the matrix model ones and discuss the nature of gravitational dressing for this regularization. Finally, we address the question of boundary conditions within the framework of the d=1 unitary matrix model, considered as a regularized version of the Hermitian model, and study the implications of a generalized action with an additional parameter (analogous to the θ parameter) which give rise to quasi-periodic wave functions.

scholarly journals Discrete Painlevé system associated with Unitary matrix model

2019 ◽  
Vol 1194 ◽  
pp. 012050
Author(s):  
Hiroshi Itoyama ◽  
Takeshi Oota ◽  
Katsuya Yano
Keyword(s):  
Matrix Model ◽  
Unitary Matrix

scholarly journals A unitary matrix model for q-deformed Plancherel growth

2021 ◽  
pp. 115531
Author(s):  
Suvankar Dutta ◽  
Debangshu Mukherjee ◽  
Neetu ◽  
Sanhita Parihar
Keyword(s):  
Matrix Model ◽  
Unitary Matrix

INTEGRABLE STRUCTURES OF UNITARY MATRIX MODELS

1992 ◽  
Vol 07 (20) ◽  
pp. 4803-4824 ◽  
Author(s):  
S. KHARCHEV ◽  
A. MIRONOV
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Toda Lattice ◽  
Discrete Analog ◽  
Unitary Matrix ◽  
Component Systems ◽  
Unitary Model ◽  
Two Component Systems ◽  
Hermitian Matrix Model ◽  
Toda Lattice Hierarchy

The unitary matrix model is considered from the viewpoint of integrability. We demonstrate that this is an integrable system embedded into a two-dimensional Toda lattice hierarchy which corresponds to an integrable chain (modified Volterra) under a special reduction. The interrelations between this chain and other chains (like the Toda one) are demonstrated to be given by Bäcklund transformations. The case of the symmetric unitary model is discussed in detail and demonstrated to be connected with the Hermitian matrix model. This connection as a discrete analog of the correspondence between KdV and MKdV systems is investigated more thoroughly. We also demonstrate that unitary matrix models can be considered as two-component systems as well.

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