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

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.

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.

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 q-Virasoro constraints in matrix models

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

RENORMALIZATION GROUP AND VIRASORO CONSTRAINTS IN LIOUVILLE FIELD THEORIES

1991 ◽  
Vol 06 (25) ◽  
pp. 2289-2300 ◽  
Author(s):  
TAKAHIRO KUBOTA ◽  
YI-XIN CHENG
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Matrix Models ◽  
Liouville Theory ◽  
Target Space ◽  
Field Theories ◽  
Renormalization Group Flow ◽  
Virasoro Constraints ◽  
Group Flow ◽  
Matter Fields

The idea of Wilson's renormalization group is applied to the 2-dimensional Liouville theory coupled to matter fields. The Virasoro structures including those of Liouville field are explicitly derived at the fixed point of the renormalization group flow. The Virasoro operators are transformed into another set of Virasoro operators acting in the target space and it is argued that the latter could be interpreted as those discovered recently in matrix models.

scholarly journals Generalized Witt, Witt n-algebras, Virasoro algebras and KdV equations induced from ℛ(p,q)-deformed quantum algebras

2020 ◽  
pp. 2150011
Author(s):  
Mahouton Norbert Hounkonnou ◽  
Fridolin Melong ◽  
Melanija Mitrović
Keyword(s):  
Matrix Models ◽  
Quantum Algebras ◽  
Kdv Equations ◽  
Virasoro Constraints ◽  
De Vries ◽  
Math Phys

We perform generalizations of Witt and Virasoro algebras, and derive the corresponding Korteweg–de Vries equations from known [Formula: see text]-deformed quantum algebras previously introduced in J. Math. Phys. 51 (2010) 063518. Related relevant properties are investigated and discussed. Besides, we construct the [Formula: see text]-deformed Witt [Formula: see text]-algebra, and determine the Virasoro constraints for a toy model, which play an important role in the study of matrix models. Finally, as a matter of illustration, explicit results are provided for the main particular deformed quantum algebras known in the literature.

PROPERTIES OF HERMITIAN MATRIX MODELS IN AN EXTERNAL FIELD

1991 ◽  
Vol 06 (37) ◽  
pp. 3455-3466 ◽  
Author(s):  
YU. MAKEENKO ◽  
G. W. SEMENOFF
Keyword(s):  
Integral Equation ◽  
Partition Function ◽  
External Field ◽  
Matrix Models ◽  
Matrix Model ◽  
Hermitian Matrix ◽  
Genus Zero ◽  
Virasoro Constraints ◽  
Large N ◽  
Single Integral

We consider a Hermitian one-matrix model in an (Hermitian) external field. We drive the Schwinger-Dyson equations and show that those can be represented as a set of Virasoro constraints which are imposed on the partition function. We prove that these Virasoro constraints are equivalent (at least at large N) to a single integral equation whose solution can be found. We use this solution to study properties of the Kontsevich model in genus zero.

scholarly journals UNITARY MATRIX MODELS AND PAINLEVÉ III

1996 ◽  
Vol 11 (38) ◽  
pp. 3001-3010 ◽  
Author(s):  
MASATO HISAKADO
Keyword(s):  
Matrix Models ◽  
Complex Conjugate ◽  
Unitary Matrix ◽  
Radial Coordinate ◽  
Integrable Equations ◽  
Virasoro Constraints ◽  
Special Case ◽  
Toda Equations

We discussed the full unitary matrix models from the viewpoints of integrable equations and string equations. Coupling the Toda equations and the string equations, we derive a special case of the Painlevé III equation. From the Virasoro constraints, we can use the radial coordinate. The relation between t1 and t−1 is like the complex conjugate.

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