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

1998 ◽  
Vol 520 (1-2) ◽  
pp. 411-432
Author(s):  
S Balaska
Keyword(s):  
Matrix Model ◽  
Critical Points ◽  
Scaling Limit ◽  
Continuous Series ◽  
Double Scaling Limit

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 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 MATRIX MODELS AND INTEGRABLE C<1 OPEN STRING THEORIES

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 ◽  
Double Scaling Limit

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

1991 ◽  
Vol 06 (09) ◽  
pp. 811-818 ◽  
Author(s):  
WAICHI OGURA
Keyword(s):  
Orthogonal Polynomial ◽  
Matrix Model ◽  
Polynomial Identity ◽  
Hermitian Matrix ◽  
Scaling Limit ◽  
String Equation ◽  
Singular Potentials ◽  
Hermitian Matrix Model ◽  
Double Scaling Limit

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

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.

THE PENNER MATRIX MODEL AND c = 1 STRINGS

1991 ◽  
Vol 06 (18) ◽  
pp. 1665-1677 ◽  
Author(s):  
S. CHAUDHURI ◽  
H. DYKSTRA ◽  
J. LYKKEN
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Matrix Model ◽  
Critical Radius ◽  
Scaling Limit ◽  
Legendre Transform ◽  
Complex Eigenvalue ◽  
Closed Contour ◽  
Branch Points ◽  
Double Scaling Limit

The steepest descent solution of the Penner matrix model has a one-cut eigenvalue support. Criticality results when the two branch points of this support coalesce. The support is then a closed contour in the complex eigenvalue plane. Simple generalizations of the Penner model have multi-cut solutions. For these models, the eigenvalue support at criticality is also a closed contour, but consisting of several cuts. We solve the simplest such model, which we call the KT model, in the double-scaling limit. Its free energy is a Legendre transform of the free energy of the c = 1 string compactified to the critical radius of the Kosterlitz–Thouless phase transition.

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