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 …

6.1. 3. Evaluation of the partition function 252 A. 2. Supersymmetric quantum mechanics 319
6.1. 4. Evaluation ofthe observables: knot A. 3. Topological sigma models 320 invariants 255 …

We present exact results for partition functions of Jackiw-Teitelboim (JT) gravity on two-
dimensional surfaces of arbitrary genus with an arbitrary number of boundaries. The …

Quantum gravity poses the problem of merging quantum mechanics and general relativity,
the two great conceptual revolutions in the physics of the twentieth century. The loop and …

These are notes based on two lectures given at the Conference on Geometry and Topology
(Harvard University, April 1990). The first was mainly devoted to explaining a conjecture …

Field theories of closed strings are shown to be exactly solvable for a central charge of
matter fields c= 1− 6/m (m+ 1), m= 1, 2, 3,…. The two-point function χ (λ, N), in which λ is the …

Starting from the random triangulation definition of two-dimensional euclidean quantum
gravity, we define the continuum limit and compute the partition function for closed surfaces …

The coupling of conformal field theories to 2-d gravity may be studied in the conformal
gauge. As an application, the results of Knizhnik, Polyakov and Zamolodchikov for the …

We propose a nonperturbative definition of two-dimensional quantum gravity, based on a
double-scaling limit of the random-matrix model. We derive an exact differential equation for …

We consider the recently proposed analytic expression for the three-point function in the
Liouville field theory on a sphere. It is verified that in the classical limit this expression …