scholarly journals Multicritical points of unitary matrix model with logarithmic potential identified with Argyres–Douglas points

2020 ◽  
Vol 35 (24) ◽  
pp. 2050146 ◽  
Author(s):  
H. Itoyama ◽  
T. Oota ◽  
Katsuya Yano
Keyword(s):  
Matrix Model ◽  
Spectral Curve ◽  
Scaling Limit ◽  
Logarithmic Potential ◽  
Unitary Matrix ◽  
Logarithmic Term ◽  
Multicritical Points ◽  
Painlevé Ii ◽  
Supersymmetric Gauge ◽  
Discrete Painlevé Equation

In our recent publications, the partition function of the Gross–Witten–Wadia unitary matrix model with the logarithmic term has been identified with the [Formula: see text] function of a certain Painlevé system, and the double scaling limit of the associated discrete Painlevé equation to the critical point provides us with the Painlevé II equation. This limit captures the critical behavior of the [Formula: see text], [Formula: see text], [Formula: see text] supersymmetric gauge theory around its Argyres–Douglas 4D superconformal point. Here, we consider further extension of the model that contains the [Formula: see text]th multicritical point and that is to be identified with [Formula: see text] theory. In the [Formula: see text] case, we derive a system of two ODEs for the scaling functions to the free energy, the time variable being the scaled total mass and make a consistency check on the spectral curve on this matrix model.

scholarly journals Theory space of one unitary matrix model and its critical behavior associated with Argyres–Douglas theory

2021 ◽  
Author(s):  
H. Itoyama ◽  
Katsuya Yano
Keyword(s):  
Matrix Model ◽  
Critical Points ◽  
Critical Behavior ◽  
Scaling Limit ◽  
Vacuum Expectation ◽  
Logarithmic Potential ◽  
Unitary Matrix ◽  
Expectation Values ◽  
Painlevé Ii ◽  
Double Scaling Limit

The lowest critical point of one unitary matrix model with cosine plus logarithmic potential is known to correspond with the [Formula: see text] Argyres–Douglas (AD) theory and its double scaling limit derives the Painlevé II equation with parameter. Here, we consider the critical points associated with all cosine potentials and determine the scaling operators, their vacuum expectation values (vevs) and their scaling dimensions from perturbed string equations at planar level. These dimensions agree with those of [Formula: see text] AD theory.

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

scholarly journals NON-PERTURBATIVE SOLUTION OF THE SUPER-VIRASORO CONSTRAINTS

1993 ◽  
Vol 08 (13) ◽  
pp. 1205-1214 ◽  
Author(s):  
K. BECKER ◽  
M. BECKER
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Scaling Limit ◽  
Virasoro Constraints ◽  
Perturbative Solution ◽  
The One ◽  
Genus Expansion ◽  
Double Scaling Limit

We present the solution of the discrete super-Virasoro constraints to all orders of the genus expansion. Integrating over the fermionic variables we get a representation of the partition function in terms of the one-matrix model. We also obtain the non-perturbative solution of the super-Virasoro constraints in the double scaling limit but do not find agreement between our flows and the known supersymmetric extensions of KdV.

scholarly journals AN OPERATOR FORMALISM FOR UNITARY MATRIX MODELS

1991 ◽  
Vol 06 (29) ◽  
pp. 2727-2739 ◽  
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.

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

scholarly journals Quantum spectral curve for (q, t)-matrix model

2017 ◽  
Vol 108 (2) ◽  
pp. 413-424 ◽  
Author(s):  
Yegor Zenkevich
Keyword(s):  
Matrix Model ◽  
Spectral Curve ◽  
T Matrix
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