Related papers: On Correlation Numbers in 2D Minimal Gravity and M…
We construct the one matrix model (MM) correlators corresponding to the general bulk-boundary correlation numbers of the minimal Liouville gravity (LG) on the disc. To find agreement between both discrete and continuous approach, we…
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…
The four-point integral of the minimal super Liouville gravity on the sphere is evaluated numerically. The integration procedure is based on the effective elliptic parameterization of the moduli space. The analysis is performed for a few…
We calculate a class of two-point boundary correlators in 2D quantum gravity using its microscopic realization as loop gas on a random surface. We find a perfect agreement with the two-point boundary correlation function in Liouville…
There are two alternative approaches to the minimal gravity - direct Liouville approach and matrix models. Recently there has been a certain progress in the matrix model approach, growing out of presence of a Frobenius manifold (FM)…
The five-point correlation numbers in the One-matrix model is calculated in the Liouville frame. Validity of the fusion rules for it is checked.
We study the boundary correlation functions in Liouville theory and in solvable statistical models of 2D quantum gravity. In Liouville theory we derive functional identities for all fundamental boundary structure constants, similar to the…
We study two-dimensional Liouville gravity and minimal string theory on spaces with fixed length boundaries. We find explicit formulas describing the gravitational dressing of bulk and boundary correlators in the disk. Their structure has a…
We review the derivation of the Liouville action in 2DQG via the trace anomaly and emphasize how a similar approach can be used to derive an effective action describing the long wavelength dynamics of the conformal factor in 4D. In 2D we…
The Liouville action for two--dimensional quantum gravity coupled to interacting matter contains terms that have not been considered previously. They are crucial for understanding the renormalization group flow and can be observed in recent…
We study the simplest examples of minimal string theory whose worldsheet description is the unitary (p,q) minimal model coupled to two-dimensional gravity (Liouville field theory). In the Liouville sector, we show that four-point…
After giving a pedagogical review of the chiral gauge approach to 2D gravity, with particular emphasis on the derivation of the gravitational Ward identities, we discuss in some detail the interpretation of matter correlation functions…
The three-point functions for minimal models coupled to gravity are derived in the operator approach to Liouville theory which is based on its $U_q(sl(2))$ quantum group structure. The result is shown to agree with matrix-model calculations…
The main results for the two-dimensional quantum gravity, conjectured from the matrix model or integrable approach, are presented in the form to be compared with the world-sheet or Liouville approach. In spherical limit the integrable side…
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…
The Liouville approach is applied to the quantum treatment of the dilaton gravity in two dimensions. The physical states are obtained from the BRST cohomology and correlation functions are computed up to three-point functions. For the $N=0$…
Liouville field theory on a sphere is considered. We explicitly derive a differential equation for four-point correlation functions with one degenerate field $V_{-\frac{mb}{2}}$. We introduce and study also a class of four-point conformal…
The Ward identities of the Liouville gravity coupled to the minimal conformal matter are investigated. We introduce the pseudo-null fields and the generalized equations of motion, which are classified into series of the Liouville charges.…
We calculate correlation functions in matrix models modified by trace-squared terms. First we study scaling operators in modified one-matrix models and find that their correlation functions satisfy modified Virasoro constraints. Then we…
The continuum (Liouville) approach to the two-dimensional (2-D) quantum gravity is reviewed with particular attention to the $c=1$ conformal matter coupling, and new results on a related problem of dilaton gravity are reported. After…