scholarly journals (Multi)matrix models and interacting clones of Liouville gravity

2008 ◽  
Vol 2008 (08) ◽  
pp. 044-044 ◽  
Author(s):  
Elias Kiritsis ◽  
Vasilis Niarchos
Keyword(s):  
Matrix Models ◽  
Liouville Gravity

Wormholes, matrix models, and liouville gravity

1996 ◽  
Vol 45 (2-3) ◽  
pp. 135-148 ◽  
Author(s):  
Igor R. Klebanov ◽  
Akikazu Hashimoto
Keyword(s):  
Matrix Models ◽  
Liouville Gravity

scholarly journals Boundary operators in minimal Liouville gravity and matrix models

2010 ◽  
Vol 2010 (12) ◽  
Author(s):  
Jean-Emile Bourgine ◽  
Goro Ishiki ◽  
Chaiho Rim
Keyword(s):  
Matrix Models ◽  
Liouville Gravity ◽  
Boundary Operators

scholarly journals 2D GRAVITY AND MATRIX MODELS I: 2D GRAVITY

1994 ◽  
Vol 09 (25) ◽  
pp. 4355-4405 ◽  
Author(s):  
A. MIRONOV
Keyword(s):  
Matrix Models ◽  
2D Gravity ◽  
Liouville Gravity ◽  
Technical Details ◽  
Almost All ◽  
Topological Theories

Some approaches to 2D gravity which have been developed in the last few years are reviewed. They are physical (Liouville) gravity, topological theories and matrix models. Special attention is paid to matrix models and their interrelations with different approaches. Almost all technical details are omitted, but examples are presented.

Two-dimensional quantum gravity

2018 ◽  
Author(s):  
Leonid Chekhov
Keyword(s):  
Quantum Gravity ◽  
Matrix Models ◽  
Matrix Model ◽  
Planar Graphs ◽  
2D Gravity ◽  
Loop Model ◽  
World Sheet ◽  
Liouville Gravity ◽  
Large N ◽  
The One

This article discusses the connection between large N matrix models and critical phenomena on lattices with fluctuating geometry, with particular emphasis on the solvable models of 2D lattice quantum gravity and how they are related to matrix models. It first provides an overview of the continuum world sheet theory and the Liouville gravity before deriving the Knizhnik-Polyakov-Zamolodchikov scaling relation. It then describes the simplest model of 2D gravity and the corresponding matrix model, along with the vertex/height integrable models on planar graphs and their mapping to matrix models. It also considers the discretization of the path integral over metrics, the solution of pure lattice gravity using the one-matrix model, the construction of the Ising model coupled to 2D gravity discretized on planar graphs, the O(n) loop model, the six-vertex model, the q-state Potts model, and solid-on-solid and ADE matrix models.

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 Fermi gas approach to general rank theories and quantum curves

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Naotaka Kubo
Keyword(s):  
Matrix Models ◽  
Critical Role ◽  
Three Dimensional ◽  
Fermi Gas ◽  
Fermi Gases ◽  
Partition Functions ◽  
Density Matrices ◽  
General Rank ◽  
Chern Simons ◽  
The Ideal

Abstract It is known that matrix models computing the partition functions of three-dimensional $$ \mathcal{N} $$ N = 4 superconformal Chern-Simons theories described by circular quiver diagrams can be written as the partition functions of ideal Fermi gases when all the nodes have equal ranks. We extend this approach to rank deformed theories. The resulting matrix models factorize into factors depending only on the relative ranks in addition to the Fermi gas factors. We find that this factorization plays a critical role in showing the equality of the partition functions of dual theories related by the Hanany-Witten transition. Furthermore, we show that the inverses of the density matrices of the ideal Fermi gases can be simplified and regarded as quantum curves as in the case without rank deformations. We also comment on four nodes theories using our results.

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