SOLITON EQUATIONS, MINIMAL KAZAMA-SUZUKI MODELS AND 2-DIMENSIONAL GRAVITY

1992 ◽  
Vol 07 (20) ◽  
pp. 4871-4883 ◽  
Author(s):  
JAN LACKI
Keyword(s):  
Matrix Models ◽  
Soliton Equations ◽  
Virasoro Constraints ◽  
Chiral Rings ◽  
Affine Algebras ◽  
Dimensional Gravity ◽  
K Matrix

We propose a framework relating the integrable structures appearing in k-matrix models with algebraic data of the corresponding N=2 Kazama-Suzuki models. Both the generalized KdV flows and the Virasoro constraints are obtained. The carrier spaces of the basic, principally realized representations of the corresponding affine algebras [Formula: see text] appear to constitute natural infinite “gravitational” analogs of the chiral rings of the associated Kazama-Suzuki models.

scholarly journals Solving Virasoro constraints in matrix models

2005 ◽  
Vol 53 (5-6) ◽  
pp. 512-521 ◽  
Author(s):  
A. Alexandrov ◽  
A. Mironov ◽  
A. Morozov
Keyword(s):  
Matrix Models ◽  
Virasoro Constraints

A COMPACT BOSON COUPLED TO TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (15) ◽  
pp. 2743-2754 ◽  
Author(s):  
NORISUKE SAKAI ◽  
YOSHIAKI TANII
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Riemann Surfaces ◽  
Partition Functions ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
The Continuum ◽  
Continuum Field

The radius dependence of partition functions is explicitly evaluated in the continuum field theory of a compactified boson, interacting with two-dimensional quantum gravity (noncritical string) on Riemann surfaces for the first few genera. The partition function for the torus is found to be a sum of terms proportional to R and 1/R. This is in agreement with the result of a discretized version (matrix models), but is quite different from the critical string. The supersymmetric case is also explicitly evaluated.

Correlators in the β-deformed Gaussian Hermitian and complex matrix models

2019 ◽  
Vol 34 (33) ◽  
pp. 1950221 ◽  
Author(s):  
Ying Chen ◽  
Bei Kang ◽  
Min-Li Li ◽  
Li-Fang Wang ◽  
Chun-Hong Zhang
Keyword(s):  
Matrix Models ◽  
Integral Representations ◽  
Witt Algebra ◽  
Complex Matrix ◽  
Virasoro Constraints

We investigate the [Formula: see text]-deformed Gaussian Hermitian and [Formula: see text] complex matrix models which are defined as the eigenvalue integral representations. Their [Formula: see text] constraints are constructed such that the constraint operators yield the same [Formula: see text][Formula: see text]-algebra. When particularized to the Virasoro constraints in the [Formula: see text] constraints, the corresponding constraint operators yield the Witt algebra and null 3-algebra. By solving our Virasoro constraints, we derive the formulas for correlators in these two [Formula: see text]-deformed matrix models, respectively.

scholarly journals ON THE SCHWINGER–DYSON EQUATIONS FOR A VERTEX MODEL COUPLED TO 2-D GRAVITY

1995 ◽  
Vol 10 (08) ◽  
pp. 695-707
Author(s):  
AL. KAVALOV
Keyword(s):  
Matrix Models ◽  
Extrinsic Curvature ◽  
Vertex Model ◽  
Point Function ◽  
Lattice Gauge ◽  
Planar Limit ◽  
Dimensional Gravity ◽  
Free Case ◽  
Lattice Gauge Theories ◽  
Perturbative Corrections

We consider a two-matrix model with the interaction involving the term tr ABAB, which is quartic in angular variables. It describes a vertex model (in particular — of F-model type) on the lattice of fluctuating geometry and is the simplest representative of the class of matrix models describing coupling to two-dimensional gravity of general vertex models. This class includes most of the physically interesting matrix models, such as lattice gauge theories and matrix models describing extrinsic curvature strings. We show that the system of loop (Schwinger–Dyson) equations of the model decouples in the planar limit and allows one to find closed equations for arbitrary correlators, including the ones involving angular variables. We write down the equations for the two-point function and the eigenvalue density and sketch the calculation of perturbative corrections to the free case

Random matrix theory and integrable systems

2018 ◽  
Author(s):  
Alexander R. Its
Keyword(s):  
Orthogonal Polynomials ◽  
Matrix Models ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Integrable Systems ◽  
Matrix Theory ◽  
Kp Hierarchy ◽  
Brownian Motions ◽  
Airy Process ◽  
Virasoro Constraints

This article discusses the interaction between random matrix theory (RMT) and integrable theory, leading to ordinary and partial differential equations (PDEs) for the eigenvalue distribution of random matrix models of size n and the transition probabilities of non-intersecting Brownian motion models, for finite n and for n → ∞. It first provides an overview of the connection between the theory of orthogonal polynomials and the KP-hierarchy in integrable systems before examining matrix models and the Virasoro constraints. It then considers multiple orthogonal polynomials, taking into account non-intersecting Brownian motions on ℝ (Dyson’s Brownian motions), a moment matrix for several weights, Virasoro constraints, and a PDE for non-intersecting Brownian motions. It also analyses critical diffusions, with particular emphasis on the Airy process, the Pearcey process, and Airy process with wanderers. Finally, it describes the Tacnode process, along with kernels and p-reduced KP-hierarchy.

Matrix models of two-dimensional gravity and Toda theory

1991 ◽  
Vol 357 (2-3) ◽  
pp. 565-618 ◽  
Author(s):  
A. Gerasimov ◽  
A. Marshakov ◽  
A. Mironov ◽  
A. Morozov ◽  
A. Orlov
Keyword(s):  
Matrix Models ◽  
Two Dimensional ◽  
Dimensional Gravity

scholarly journals MATRIX MODELS OF TWO-DIMENSIONAL GRAVITY AND DISCRETE TODA THEORY

1996 ◽  
Vol 11 (22) ◽  
pp. 1797-1806 ◽  
Author(s):  
MASATO HISAKADO ◽  
MIKI WADATI
Keyword(s):  
Discrete Time ◽  
Matrix Model ◽  
Scaling Limit ◽  
Toda Chain ◽  
Partition Functions ◽  
Two Dimensional ◽  
Virasoro Constraints ◽  
The Matrix ◽  
Dimensional Gravity ◽  
Molecule Equation

Recursion relations for orthogonal polynomials, arising in the study of one-matrix model of two-dimensional gravity, are shown to be equivalent to the equations of the Toda-chain hierarchy supplemented by additional Virasoro constraints. This is the case without the double scaling limit. A discrete time variable to the matrix model is introduced. The discrete time dependent partition functions are given by τ functions which satisfy the discrete Toda molecule equation. Further the relations between the matrix model and the discrete time Toda theory are discussed.

scholarly journals q-Virasoro constraints in matrix models

2017 ◽  
Vol 2017 (3) ◽  
Author(s):  
Anton Nedelin ◽  
Maxim Zabzine
Keyword(s):  
Matrix Models ◽  
Virasoro Constraints
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