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

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.

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

International Journal of Modern Physics A ◽

10.1142/s0217751x20501468 ◽

2020 ◽

Vol 35 (24) ◽

pp. 2050146 ◽

Cited By ~ 1

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.

The continuous series of critical points of the two-matrix model at N → ∞ in the double scaling limit

Nuclear Physics B ◽

10.1016/s0550-3213(98)00080-7 ◽

1998 ◽

Vol 520 (1-2) ◽

pp. 411-432

Author(s):

S Balaska

Keyword(s):

Matrix Model ◽

Critical Points ◽

Scaling Limit ◽

Continuous Series ◽

NON-PERTURBATIVE SOLUTION OF THE SUPER-VIRASORO CONSTRAINTS

10.1142/s0217732393002695 ◽

1993 ◽

Vol 08 (13) ◽

pp. 1205-1214 ◽

Cited By ~ 38

Author(s):

K. BECKER ◽

M. BECKER

Keyword(s):

Partition Function ◽

Matrix Model ◽

Scaling Limit ◽

Virasoro Constraints ◽

Perturbative Solution ◽

The One ◽

Genus Expansion ◽

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.

Discrete Painlevé system and the double scaling limit of the matrix model for irregular conformal block and gauge theory

Physics Letters B ◽

10.1016/j.physletb.2018.10.077 ◽

2019 ◽

Vol 789 ◽

pp. 605-609 ◽

Cited By ~ 2

Author(s):

H. Itoyama ◽

T. Oota ◽

Katsuya Yano

Keyword(s):

Gauge Theory ◽

Matrix Model ◽

Scaling Limit ◽

Conformal Block ◽

The Matrix ◽

AN OPERATOR FORMALISM FOR UNITARY MATRIX MODELS

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 ◽

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.

Numerical analysis of the double scaling limit in the bosonic part of the II-B matrix model

Nuclear Physics B - Proceedings Supplements ◽

10.1016/s0920-5632(01)00884-2 ◽

2001 ◽

Vol 94 (1-3) ◽

pp. 708-710

Author(s):

S. Horata ◽

H.S. Egawa

Keyword(s):

Numerical Analysis ◽

Matrix Model ◽

Scaling Limit ◽

Bosonic Part ◽

A possible IIB superstring matrix model with Euler characteristic and a double scaling limit

Physics Letters B ◽

10.1016/s0370-2693(97)00597-2 ◽

1997 ◽

Vol 405 (1-2) ◽

pp. 45-48 ◽

Cited By ~ 6

Author(s):

C.F. Kristjansen ◽

P. Olesen

Keyword(s):

Euler Characteristic ◽

Matrix Model ◽

Scaling Limit ◽

MATRIX MODELS AND INTEGRABLE C<1 OPEN STRING THEORIES

International Journal of Modern Physics D ◽

10.1142/s0218271894000290 ◽

1994 ◽

Vol 03 (01) ◽

pp. 203-206

Author(s):

LAURENT HOUART

Keyword(s):

Ising Model ◽

Boundary Conditions ◽

Matrix Models ◽

Matrix Model ◽

Scaling Limit ◽

Open String ◽

String Equation ◽

Random Surfaces ◽

Ising Spins ◽

We study in the double scaling limit the two-matrix model which represents the sum over closed and open random surfaces coupled to an Ising model. The boundary conditions are characterized by the fact that the Ising spins sitting at the vertices of the boundaries are all in the same state. We obtain the string equation.

MAPPING BETWEEN TODA AND KDV FLOWS IN THE HERMITIAN MATRIX MODEL

10.1142/s0217732391000841 ◽

1991 ◽

Vol 06 (09) ◽

pp. 811-818 ◽

Cited By ~ 1

Author(s):

WAICHI OGURA

Keyword(s):

Orthogonal Polynomial ◽

Matrix Model ◽

Polynomial Identity ◽

Hermitian Matrix ◽

Scaling Limit ◽

String Equation ◽

Singular Potentials ◽

Hermitian Matrix Model ◽

The scaling operators are studied at finite N. We find new singular potentials for which an orthogonal polynomial identity gives the string equation at the double scaling limit. They are free from the degeneracy between even and odd potentials, and provide the mapping between the sl(∞) Toda and the generalized KdV flows. The degeneracy in formal Virasoro conditions are derived explicitly.

UNIVERSALITY OF THE MATRIX MODEL APPROACH TO TWO-DIMENSIONAL QUANTUM GRAVITY

10.1142/s0217732391001482 ◽

1991 ◽

Vol 06 (15) ◽

pp. 1387-1396

Author(s):

FREDDY PERMANA ZEN

Keyword(s):

Quantum Gravity ◽

Matrix Model ◽

Scaling Limit ◽

Numerical Calculations ◽

Two Dimensional ◽

Coupled Equations ◽

The Matrix ◽

Pure Gravity ◽

Double Scaling Limit ◽

Model Approach

Universality with respect to triangulations is investigated in the Hermitian one-matrix model approach to 2-D quantum gravity for a potential containing both even and odd terms, [Formula: see text]. With the use of analytical and numerical calculations, I find that the universality holds and the model describes pure gravity, which leads in the double scaling limit to coupled equations of Painlevé type.