Matrix model approach to minimal Liouville gravity revisited

Abstract

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 model that intrinsically contains information about the conformal selection rules. We discuss how to modify the Frobenius manifold structure appropriately for this purposes. We propose a modification of the construction for Lee-Yang series involving the $A_{p-1}$ algebra instead of the previously used $A_1$ algebra. With the new prescription, we calculate correlators on the sphere up to four points and find full agreement with the continuous approach without using resonance transformations.

arXiv comment11 pages

References in corpus (5)

• Higher Equations of Motion in Liouville Field Theory
• Minimal Liouville Gravity correlation numbers from Douglas string equation
• Unitary Minimal Liouville Gravity and Frobenius Manifolds
• Frobenius manifolds, Integrable Hierarchies and Minimal Liouville Gravity
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Cited by in corpus (9)

• Notes on Matrix Models
• Open minimal strings and open Gelfand-Dickey hierarchies
• Minimal gravity and Frobenius manifolds: bulk correlation on sphere and disk
• Flat coordinates for Saito Frobenius manifolds and String theory
• From minimal gravity to open intersection theory
• $x-y$ swap for $(2,2p+1)$ minimal string
• Dual Frobenius manifolds of minimal gravity on disk
• On exact solution of topological CFT models based on Kazama-Suzuki cosets
• Resonance transformations for the $(2,2p+1)$ minimal string via $x-y$ swap: a proof of Artemev's conjecture