2D Gravity and Matrix Models

2000 ◽  
pp. 346-384
Author(s):  
Michio Kaku
Keyword(s):  
Matrix Models ◽  
2D Gravity

scholarly journals INTEGRABLE STRUCTURES IN MATRIX MODELS AND PHYSICS OF 2D GRAVITY

1993 ◽  
Vol 08 (22) ◽  
pp. 3831-3882 ◽  
Author(s):  
A. MARSHAKOV
Keyword(s):  
Field Theory ◽  
Matrix Models ◽  
Matrix Model ◽  
2D Gravity ◽  
Model Description ◽  
Physical Role ◽  
Theory Formulation ◽  
The Matrix ◽  
Free Fields ◽  
Effective Description

A review of the appearance of integrable structures in the matrix model description of 2D gravity is presented. Most of the ideas are demonstrated with technically simple but ideologically important examples. Matrix models are considered as a sort of “effective” description of continuum 2D field theory formulation. The main physical role in such a description is played by the Virasoro-W conditions, which can be interpreted as certain unitarity or factorization constraints. Both discrete and continuum (generalized Kontsevich) models are formulated as the solutions to those discrete (continuous) Virasoro-W constraints. Their integrability properties are proved, using mostly the determinant technique highly related to the representation in terms of free fields. The paper also contains some new observations connected with formulation of more-general-than-GKM solutions and deeper understanding of their relation to 2D gravity.

Instability of even m multicritical matrix models of 2D gravity

1991 ◽  
Vol 253 (3-4) ◽  
pp. 292-296 ◽  
Author(s):  
Simon Dalley
Keyword(s):  
Matrix Models ◽  
2D Gravity

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.

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