Related papers: A remark on the three approaches to 2D Quantum gra…
One-matrix model in $p$-critical point on torus is considered. The generating function of correlation numbers in genus one is evaluated and used for computation correlation numbers in KdV and CFT frames. It is shown that the correlation…
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…
A topological procedure for computing correlation functions for any (1,q) model is presented. Our procedure can be used to compute any correlation function on the sphere as well as some correlation functions at higher genus. We derive new…
We evaluate the three point function for arbitrary states in bosonic minimal models on the sphere coupled to quantum gravity in two dimensions. The validity of the formal continuation in the number of Liouville screening charge insertions…
We compute N-point correlation functions of non-unitary (2k-1, 2) minimal matter coupled to 2D quantum gravity on a sphere using the continuum Liouville field approach. A gravitational dressing of the matter primary field with the minimum…
We consider a model of 2D gravity with the action quadratic in curvature and represent path integrals as integrals over the SL(2, R) invariant Gaussian functional measure. We reduce these path integrals to the products of Wiener path…
In the first part of the talk, I review the applications of loop equations to the matrix models and to 2-dimensional quantum gravity which is defined as their continuum limit. The results concerning multi-loop correlators for low genera and…
In this paper we use recent results on resonance relations between the matrix models and the minimal Liouville gravity to compute the torus correlation numbers in (3,p) minimal Liouville gravity. Namely, we calculate the torus generating…
We review recent progress in 2D gravity coupled to $d<1$ conformal matter, based on a representation of discrete gravity in terms of random matrices. We discuss the saddle point approximation for these models, including a class of related…
We test recent results for the four-point correlation numbers in Minimal Liouville Gravity against calculations in the one-Matrix Models, and find full agreement. In the process, we construct the resonance transformation which relates…
A classical two dimensional theory of gravity which has a number of interesting features (including a Newtonian limit, black holes and gravitational collapse) is quantized using conformal field theoretic techniques. The critical dimension…
We study the boundary correlation functions in Liouville theory and in solvable statistical models of 2D quantum gravity. In Liouville theory we derive functional identities for all fundamental boundary structure constants, similar to the…
We show how to formulate a lattice gauge theory whose naive continuum limit corresponds to two-dimensional (Euclidean) quantum gravity including a positive cosmological constant. More precisely the resultant continuum theory corresponds to…
We calculate a class of two-point boundary correlators in 2D quantum gravity using its microscopic realization as loop gas on a random surface. We find a perfect agreement with the two-point boundary correlation function in Liouville…
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.…
We describe the idea of studying quantum gravity by means of dynamical triangulations and give examples of its implementation in 2, 3 and 4 space time dimensions. For $d=2$ we consider the generic hermitian 1-matrix model. We introduce the…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
We formulate a non-perturbative lattice model of two-dimensional Lorentzian quantum gravity by performing the path integral over geometries with a causal structure. The model can be solved exactly at the discretized level. Its continuum…
A canonical quantization for two dimensional gravity models, including a dilaton gravity model, is performed in a way suitable for the light-cone gauge. We extend the theory developed by Abdalla {\it et.al.}\cite{AM} and obtain the…
One-dimensional topological gravity is defined as a Gaussian integral as its partition function. The Gaussian integral supplies a toy model as a simpler version of one-matrix model that is well known to provide a description of…