scholarly journals Spectral Curves, Variational Problems and the Hermitian Matrix Model with External Source

2021 ◽  
Vol 383 (3) ◽  
pp. 2163-2242
Author(s):  
Andrei Martínez-Finkelshtein ◽  
Guilherme L. F. Silva
Keyword(s):  
Matrix Model ◽  
Hermitian Matrix ◽  
Variational Problems ◽  
External Source ◽  
Spectral Curves ◽  
Hermitian Matrix Model

scholarly journals Genus expansion of matrix models and ћ expansion of KP hierarchy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
A. Andreev ◽  
A. Popolitov ◽  
A. Sleptsov ◽  
A. Zhabin
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Special Interest ◽  
Hermitian Matrix ◽  
Geometric Meaning ◽  
Kp Hierarchy ◽  
Hurwitz Numbers ◽  
Kp Equations ◽  
Genus Expansion ◽  
Hermitian Matrix Model

Abstract We study ћ expansion of the KP hierarchy following Takasaki-Takebe [1] considering several examples of matrix model τ-functions with natural genus expansion. Among the examples there are solutions of KP equations of special interest, such as generating function for simple Hurwitz numbers, Hermitian matrix model, Kontsevich model and Brezin-Gross-Witten model. We show that all these models with parameter ћ are τ-functions of the ћ-KP hierarchy and the expansion in ћ for the ћ-KP coincides with the genus expansion for these models. Furthermore, we show a connection of recent papers considering the ћ-formulation of the KP hierarchy [2, 3] with original Takasaki-Takebe approach. We find that in this approach the recovery of enumerative geometric meaning of τ-functions is straightforward and algorithmic.

scholarly journals Bulk–boundary correlators in the hermitian matrix model and minimal Liouville gravity

2012 ◽  
Vol 854 (3) ◽  
pp. 853-877 ◽  
Author(s):  
Jean-Emile Bourgine ◽  
Goro Ishiki ◽  
Chaiho Rim
Keyword(s):  
Matrix Model ◽  
Hermitian Matrix ◽  
Liouville Gravity ◽  
Hermitian Matrix Model

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.

MATHEMATICAL ASPECTS OF THE NON-PERTURBATIVE 2D QUANTUM GRAVITY

1990 ◽  
Vol 05 (25) ◽  
pp. 2079-2083 ◽  
Author(s):  
A. R. ITS ◽  
A. V. KITAEV
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Hermitian Matrix ◽  
Continuous Limit ◽  
Hermitian Matrix Model

We present rigorous mathematical results for the continuous limit for the hermitian matrix model in connection with the non-perturbative theory of 2D quantum gravity.

PROPERTIES OF LOOP EQUATIONS FOR THE HERMITIAN MATRIX MODEL AND FOR TWO-DIMENSIONAL QUANTUM GRAVITY

1990 ◽  
Vol 05 (22) ◽  
pp. 1753-1763 ◽  
Author(s):  
J. AMBJØRN ◽  
YU. M. MAKEENKO
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Hermitian Matrix ◽  
General Procedure ◽  
Iterative Solution ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Continuum Equation ◽  
Hermitian Matrix Model ◽  
The Continuum

We study the properties of the loop equations for the N × N Hermitian matrix model with arbitrary (even) interaction as well as of their continuum limit, associated with the two-dimensional quantum gravity. We apply the general procedure of iterative solution proposed recently by David. We relate the specific heat to the singular behavior of the connected correlator of two loops. We solve the continuum equation to a few lower orders in the string coupling constant, obtaining results for macroscopic loops including the case of a multicritical fixed point.

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