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 …

String Theory comprises two volumes which give a comprehensive and pedagogic account
of the subject. Volume 1, first published in 1998, provides a thorough introduction to the …

We develop techniques to compute higher loop string amplitudes for twisted N= 2 theories
with ĉ= 3 (ie the critical case). An important ingredient is the discovery of an anomaly at …

An exact conformal field theory describing a black hole in two-dimensional space-time is
found as an SL (2, openR)/U (1) gauged Wess-Zumino-Witten model. For k= 9/4, the …

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 …

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 …

The topological phase of two-dimensional gravity is re-examined. The correlation functions
of the naturally occuring operators in the minimal topological model are computed, using …

Following the discovery of spacetime anomaly cancellation in 1984 [1], string theory has
undergone rapid development in several directions. The early hope of making direct contact …

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 …