Related papers: 2D Gravity and Random Matrices
We introduce {\it conformal multi-matrix models} (CMM) as an alternative to conventional multi-matrix model description of two-dimensional gravity interacting with $c < 1$ matter. We define CMM as solutions to (discrete) extended Virasoro…
The recent progress in the Causal Dynamical Triangulations (CDT) approach to quantum gravity indicates that gravitation is nonperturbatively renormalizable. We review some of the latest results in 1+1 and 3+1 dimensions with special…
We give further evidence that the matrix-tensor model studied in \cite{belin2023} is dual to AdS$_{3}$ gravity including the sum over topologies. This provides a 3D version of the duality between JT gravity and an ensemble of random…
We naturally extend the theory of gravity with a conformally coupled scalar field by only requiring conformal invariance of the scalar field equation of motion and not of the action. The classically extended theory incorporates a…
This note aims to provide an entr\'ee to two developments in two-dimensional topological gravity -- that is, intersection theory on the moduli space of Riemann surfaces -- that have not yet become well-known among physicists. A little over…
We review some recent proposals for relativistic models of dark matter in the context of bimetric gravity. The aim is to solve the problems of cold dark matter (CDM) at galactic scales, and to reproduce the phenomenology of the modified…
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…
Warped extra dimension claims remarkable success: solving the hierarchy problem; explaining hierarchies in particle phenomenology; yielding standard cosmology, plus interesting nonstandard scenarios. Yet it has marked shortcomings: we…
Random matrices in the large N expansion and the so-called double scaling limit can be used as toy models for quantum gravity: 2D quantum gravity coupled to conformal matter. This has generated a tremendous expansion of random matrix…
Three dimensional Eddington-inspired Born--Infeld gravity is studied with the goal of finding new solutions. Beginning with cosmology, we obtain analytical and numerical solutions for the scale factor, a(t), in spatially flat (k=0) and…
The recursion relations of 2D quantum gravity coupled to the Ising model discussed by the author previously are reexamined. We study the case in which the matter sector satisfies the fusion rules and only the primary operators inside the…
A recently introduced model of dually weighted planar graphs is solved in terms of an elliptic parametrization for some particular collection of planar graphs describing the 2D $R^2$ quantum gravity. Along with the cosmological constant…
Within the first order formalism static solutions of generic dilaton gravity in 2D with self-interacting (scalar) matter can be discussed with ease. The question of (non)existence of Killing horizons is addressed and the interplay with…
A review of the appearence of integrable structures in the matrix model description of $2d$-gravity is presented. Most of ideas are demonstrated at the technically simple but ideologically important examples. Matrix models are considered as…
In this thesis we analyze a very simple model of two dimensional quantum gravity based on causal dynamical triangulations (CDT). We present an exactly solvable model which indicates that it is possible to incorporate spatial topology…
It is well known that one can parameterize 2-D Riemannian structures by conformal transformations and diffeomorphisms of fiducial constant curvature geometries; and that this construction has a natural setting in general relativity theory…
A new formulation of $c\leq 1$ matter coupled to 2D gravity is proposed. This model, being closely analogous to one in the Polyakov light-cone gauge, possesses well defined global properties which allow to calculate correlation functions.…
We introduce a new 1-matrix model with arbitrary potential and the matrix-valued background field. Its partition function is a $\tau$-function of KP-hierarchy, subjected to a kind of ${\cal L}_{-1}$-constraint. Moreover, partition function…
We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an…
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side…