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 …

We review recent developments (up to January 2004) of the Liouville field theory and its
matrix model dual. This review consists of two parts. In part I, we review the bosonic Liouville …

We review the status of Liouville field theory and discuss the identification of states and
operators. The quantum theory has two kinds of states (and operators). Local operators …

This graduate level text describes in a unified fashion the statistical mechanics of random
walks, random surfaces and random higher dimensional manifolds with an emphasis on the …

Simple random walks-or equivalently, sums of independent random vari ables-have long
been a standard topic of probability theory and mathemat ical physics. In the 1950s, non …

The first part is an introduction to conformal field theory and string perturbation theory. The
second part deals with the search for a deeper answer to the question posed in the title …

We argue that the leading weak coupling nonperturbative effects in closed string theories
should be of order exp (—C/κ) where κ 2 is the closed string coupling constant. This is the …

We propose gauging matrix models of string theory to eliminate unwanted nonsinglet states.
To this end we perform a discretized light-cone quantization of large-N gauge theory in 1+ 1 …

In these notes we explore a variety of models comprising a large number of constituents. An
emphasis is placed on integrals over large Hermitian matrices, as well as quantum …

A bstract In this paper, we introduce an\(\mathcal {N}= 1\) supersymmetric SYK model with
SO (q) global symmetry. We study the large N expansion of the bi-local collective action of …