Related papers: Minimal gravity and Frobenius manifolds: bulk corr…
We study unitary minimal models coupled to Liouville gravity using Douglas string equation. Our approach is based on the assumption that there exist an appropriate solution of the Douglas string equation and some special choice of the…
We continue to study minimal Liouville gravity (MLG) using a dual approach based on the idea that the MLG partition function is related to the tau function of the A_q integrable hierarchy via the resonance transformations, which are in turn…
Using the connection with the Frobenius manifold structure, we study the matrix model description of minimal Liouville gravity (MLG) based on the Douglas string equation. Our goal is to find an exact discrete formulation of the (q,p) MLG…
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…
We use the connection between the Frobrenius manifold and the Douglas string equation to further investigate Minimal Liouville gravity. We search a solution of the Douglas string equation and simultaneously a proper transformation from the…
Liouville field theory approach to 2-dimensional gravity possesses the duality ($b \leftrightarrow b^{-1}$). The matrix counterpart of minimal gravity $\mathcal{M}(q,p)$ ($q<p$ co-prime) is effectively described on $A_{q-1}$ Frobenius…
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 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…
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…
In this paper we use recent results on resonance relations between the matrix models and the minimal Liouville gravity to compute the torus correlation numbers in (3,p) minimal Liouville gravity. Namely, we calculate the torus generating…
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 consider bulk correlation numbers on disk in one-matrix model. Using the recently found so-called resonance transformation from the KdV to the Liouville frame, we obtain an explicit expression for the bulk one-point function. The result…
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…
We compute N-point correlation functions of non-unitary (2k-1, 2) minimal matter coupled to 2D quantum gravity on a sphere using the continuum Liouville field approach. A gravitational dressing of the matter primary field with the minimum…
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…
Motivated by recent works on the connection between 2D quantum gravity and timelike Liouville theory, we revisit the latter and clarify some aspects of the computation of its partition function: We present a detailed computation of the…
We study a two-dimensional conformal field theory coupled to quantum gravity on a disk. Using the continuum Liouville field approach, we compute three-point correlation functions of boundary operators. The structure of momentum…
Using Polyakov's functional integral approach with the Liouville action functional defined in \cite{ZT2} and \cite{LTT}, we formulate quantum Liouville theory on a compact Riemann surface X of genus g > 1. For the partition function <X> and…
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…
Using a previously developed experimental method to reduce friction in mechanically stable packings of disks, we find that frictional packings form tree-like structures of geometrical families that lie on reduced dimensional manifolds in…