On Correlation Numbers in 2D Minimal Gravity and Matrix Models

Abstract

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 coupling parameters of the Liouville Gravity with the couplings of the Matrix Models, up to the terms of the order 4. We also conjecture the general form of this transformation.

Talk presented at "Liouville Gravity and Statistical Models", International conference in memory of Alexei Zamolodchikov, Moscow, June 21-24 2008

References in corpus (4)

• 2D Gravity and Random Matrices
• Lectures on 2D gravity and 2D string theory (TASI 1992)
• World Sheet and Space Time Physics in Two Dimensional (Super) String Theory
• Higher Equations of Motion in Liouville Field Theory

Cited by in corpus (46)

• Liouville quantum gravity -- holography, JT and matrices
• Dilaton-gravity, deformations of the minimal string, and matrix models
• Solving Puzzles in Deformed JT Gravity: Phase Transitions and Non-Perturbative Effects
• The ZZ annulus one-point function in non-critical string theory: A string field theory analysis
• Minimal Liouville Gravity correlation numbers from Douglas string equation
• Random Kähler Metrics
• Universal scaling limits of matrix models, and (p,q) Liouville gravity
• Degenerate operators in JT and Liouville (super)gravity
• Boundary correlation numbers in one matrix model
• Matrix integrals $\&$ finite holography
• Unitary Minimal Liouville Gravity and Frobenius Manifolds
• Two dimensional gravity in genus one in Matrix Models, Topological and Liouville approaches
• The complex Liouville string: the worldsheet
• On the construction of the correlation numbers in Minimal Liouville Gravity
• Boundary operators in minimal Liouville gravity and matrix models
• Deformations of JT Gravity via Topological Gravity and Applications
• Torus Amplitudes in Minimal Liouville Gravity and Matrix Models
• Bulk one-point function on disk in one-matrix model
• Phase transitions for deformations of JT supergravity and matrix models
• Five-point Correlation Numbers in One-Matrix Model
• Open KdV hierarchy and minimal gravity on disk
• A remark on the three approaches to 2D Quantum gravity
• Five-point correlation numbers in minimal Liouville gravity and matrix models
• Bulk-boundary correlators in the hermitian matrix model and minimal Liouville gravity
• On two-dimensional quantum gravity and quasiclassical integrable hierarchies
• Note on large-$p$ limit of $(2,2p+1)$ minimal Liouville gravity and moduli space volumes
• Open minimal strings and open Gelfand-Dickey hierarchies
• Minimal gravity and Frobenius manifolds: bulk correlation on sphere and disk
• Boundary operators in the one-matrix model
• A Flow in the Forest
• On generalization of 2d gravity with the simplest non-invariant states
• Flat coordinates for Saito Frobenius manifolds and String theory
• Modular Integrals in Minimal Super Liouville Gravity
• A note on the Lee-Yang singularity coupled to 2d quantum gravity
• From minimal gravity to open intersection theory
• Open KdV hierarchy of 2d minimal gravity of Lee-Yang series
• Dual Frobenius manifolds of minimal gravity on disk
• $x-y$ swap for $(2,2p+1)$ minimal string
• The null identities for boundary operators in the $(2,2p+1)$ minimal gravity
• On construction of correlation numbers in super Minimal Liouville Gravity in the Ramond sector
• Boundary timelike Liouville theory: bulk 1-point & boundary 2-point functions
• Minimal Liouville Gravity on the Torus via Matrix Models
• Torus one-point correlation numbers in minimal Liouville gravity
• The semiclassical gravitational path integral and random matrices
• Resonance transformations for the $(2,2p+1)$ minimal string via $x-y$ swap: a proof of Artemev's conjecture
• Correlation functions and spectral curves in models of minimal gravity