Correlation Functions in Unitary Minimal Liouville Gravity and Frobenius Manifolds

Abstract

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 fixed by conformal selection rules. One of the main problems in this approach is to choose the solution of the Douglas string equation that is relevant for MLG. The appropriate solution was recently found using connection with the Frobenius manifolds. We use this solution to investigate three- and four-point correlators in the unitary MLG models. We find an agreement with the results of the original approach in the region of the parameters where both methods are applicable. In addition, we find that only part of the selection rules can be satisfied using the resonance transformations. The physical meaning of the nonzero correlators, which before coupling to Liouville gravity are forbidden by the selection rules, and also the modification of the dual formulation that takes this effect into account remains to be found.

arXiv comment26 pages

References in corpus (10)

• Strings with Discrete Target Space
• Gauge Invariant Matrix Model for the Â-D-Ê Closed Strings
• Bulk correlation functions in 2D quantum gravity
• Non-Rational 2D Quantum Gravity: I. World Sheet CFT
• Minimal Liouville Gravity correlation numbers from Douglas string equation
• Non-Rational 2D Quantum Gravity II. Target Space CFT
• Unitary Minimal Liouville Gravity and Frobenius Manifolds
• Frobenius manifolds, Integrable Hierarchies and Minimal Liouville Gravity
• Torus Amplitudes in Minimal Liouville Gravity and Matrix Models
• Gravitational Yang-Lee Model. Four Point Function

Cited by in corpus (6)

• Matrix model approach to minimal Liouville gravity revisited
• Open minimal strings and open Gelfand-Dickey hierarchies
• Flat structures on Frobenius Manifolds in the case of irrelevant deformations
• Minimal gravity and Frobenius manifolds: bulk correlation on sphere and disk
• Flat structures on the deformations of Gepner chiral rings
• On exact solution of topological CFT models based on Kazama-Suzuki cosets