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 …

A bstract In a series of recent papers, a special kind of AdS 2/CFT 1 duality was observed:
the boundary correlators of elementary fields that appear in the Lagrangian of a 2d …

We study N= 1 super-Liouville theory on worldsheets with and without boundary. Some
basic correlation functions on a sphere or a disc are obtained using the properties of …

A comprehensive survey of the use of the Liouville (and super-Liouville) equation in (super)
string theory outside the critical dimension, and of the complementary approach based on …

We review the relation between the matrix model and Liouville approaches to two-
dimensional gravity as elaborated by Moore, Seiberg and Staudacher. Then, based on the …

We compute correlation functions in N= 2 non-critical superstrings on the sphere. Our
calculations are restrained to the (s= 0) bulk amplitudes. We show that the four-point function …

In this paper, we first recall the approach to extract Liouville field theories from the action of
worldsheets superstring in the standard case and also in the presence of gauge fields. In …

We consider the correlation functions of the tachyon vertex operator of the super Liouville
theory coupled to matter fields in the super Coulomb gas formulation, on world sheets with …

The covariant operator quantization of the ordinary free spinning BDH string modified by
adding the supersymmetric Liouville sector is analysed in the even target space dimensions …

We discuss the structure of correlators involving the spinor emission vertex in non-critical N=
1 superstring theory. The technique used in the computation is the zero mode integration to …