Related papers: On the Liouville Approach to Correlation Functions…
The quantisation of the two-dimensional Liouville field theory is investigated using the path integral, on the sphere, in the large radius limit. The general form of the $N$-point functions of vertex operators is found and the three-point…
We calculate three- and four-point functions in super Liouville theory coupled to super Coulomb gas on world sheets with spherical topology. We first integrate over the zero mode and assume that a parameter takes an integer value. After…
The correlation functions for models of minimal gravity are discussed. An algorithm is proposed for calculations of invariant ratios from formulas of residues that can be compared with the coefficients of expansion of the partition function…
The nonlinear structures in 2D quantum gravity coupled to the $(q+1,q)$ minimal model are studied in the Liouville theory to clarify the factorization and the physical states. It is confirmed that the dressed primary states outside the…
Three-point correlation function in perturbed conformal field theory coupled to two-dimensional quantum gravity (perturbed Liouville gravity) is explicitly computed by using the free field approach. The representation considered here is the…
We develop a functional integral approach to quantum Liouville field theory completely independent of the hamiltonian approach. To this end on the sphere topology we solve the Riemann-Hilbert problem for three singularities of finite…
We address the problem of computing the tachyon correlation functions in Liouville gravity with generic (non-rational) matter central charge c<1. We consider two variants of the theory. The first is the conventional one in which the…
The computation of the correlation numbers in Minimal Liouville Gravity involves an integration over moduli spaces of complex curves. There are two independent approaches to the calculation: the direct one, based on the CFT methods and…
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…
We compare the standard and geometric approaches to quantum Liouville theory on the pseudosphere by performing perturbative calculations of the one and two point functions up to the third order in the coupling constant. The choice of the…
The one-matrix model is considered. The generating function of the correlation numbers is defined in such a way that this function coincide with the generating function of the Liouville gravity. Using the Kontsevich theorem we explain that…
In this paper, we rigorously construct $2d$ Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov "Quantum Geometry of bosonic strings". We also establish some of its fundamental properties…
We compute the three point functions of Neveu--Schwarz primary fields of the minimal models on the sphere when coupled to supergravity in two dimensions. The results show that the three point correlation functions are determined by the…
Liouville field theory has long been a cornerstone of two-dimensional quantum field theory and quantum gravity, which has attracted much recent attention in the mathematics literature. Timelike Liouville field theory is a version of…
We study semiclassical correlation functions in Liouville field theory on a two-sphere when all operators have large conformal dimensions. In the usual approach, such computation involves solving the classical Liouville equation, which is…
We discuss some classical and quantum properties of 2d gravity models involving metric and a scalar field. Different models are parametrized in terms of a scalar potential. We show that a general Liouville-type model with exponential…
The partition function corresponding to the "polytopic" action, a new action for the gravitational interaction which we have proposed recently, is computed in the simplest two-dimensional geometries of genus zero and one. The functional…
Based on a recent paper by Takhtajan, we propose a formulation of 2D quantum gravity whose basic object is the Liouville action on the Riemann sphere $\Sigma_{0,m+n}$ with both parabolic and elliptic points. The identification of the…
The recursion relations of 2D quantum gravity coupled to the Ising model discussed by the author previously are reexamined. We study the case in which the matter sector satisfies the fusion rules and only the primary operators inside the…
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…