相关论文: Matrix models of 2d gravity

A simple cubic matrix model is presented, which has truncations that, it is argued, lead at the classical level to a variety of theories of gauge fields and gravity. These include Chern-Simons theory in d=3, and BF theory and general…

In the recent years a lot of attention is focused on unconventional string compactifications. A variety of different but related frameworks was developed in order to address issues such as duality invariance, non-geometry and…

It is generally accepted that the double-scaled 1D matrix model is equivalent to the $c=1$ string theory with tachyon condensation. There remain however puzzles that are to be clarified in order to utilize this connection for our quest…

We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…

A recently introduced approach for the dynamical analysis and quantization of field theoretical models with second class constraints is ilustrated applied to linearized gravity in 3-D. The canonical structure of two different models of…

Matrix models are a highly successful framework for the analytic study of random two dimensional surfaces with applications to quantum gravity in two dimensions, string theory, conformal field theory, statistical physics in random geometry,…

Discrete approaches to gravity, both classical and quantum, are reviewed briefly, with emphasis on the method using piecewise-linear spaces. Models of 3-dimensional quantum gravity involving 6j-symbols are then described, and progress in…

We introduce a new matrix model that describes Causal Dynamical Triangulations (CDT) in two dimensions. In order to do so, we introduce a new, simpler definition of 2D CDT and show it to be equivalent to the old one. The model makes use of…

Recursion relations for orthogonal polynominals, arising in the study of the one-matrix model of two-dimensional gravity, are shown to be equvalent to the equations of the Toda-chain hierarchy supplemented by additional Virasoro…

Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…

We consider a matrix model description of the 2d string theory whose matter part is given by a time-like linear dilaton CFT. This is equivalent to the c=1 matrix model with a deformed, but very simple fermi surface. Indeed, after a Lorentz…

We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete approximation of general relativity.

Matrix models and their connections to String Theory and noncommutative geometry are discussed. Various types of matrix models are reviewed. Most of interest are IKKT and BFSS models. They are introduced as 0+0 and 1+0 dimensional reduction…

The background independent formulation of the gauge theories on D-branes in flat space-time is considered, some examples of the solutions of their equations of motion are presented, the solutions of Dirac equation in these backgrounds are…

The interaction of matter with gravity in two dimensional spacetimes can be supplemented with a geometrical force analogous to a Lorentz force produced on a surface by a constant perpendicular magnetic field. In the special case of constant…

We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…

Random matrix models encode a theory of random two dimensional surfaces with applications to string theory, conformal field theory, statistical physics in random geometry and quantum gravity in two dimensions. The key to their success lies…

We discuss how concepts such as geodesic length and the volume of space-time can appear in 2d topological gravity. We then construct a detailed mapping between the reduced Hermitian matrix model and 2d topological gravity at genus zero.…

In recent years, random matrices have come to play a major role in computational mathematics, but most of the classical areas of random matrix theory remain the province of experts. Over the last decade, with the advent of matrix…

The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Determinantal formulas, relation to conformal field models and the theory of Generalized Kontsevich model are discussed in some…