Multi-loop correlators for rational theories of 2D gravity from the generalized Kontsevich models

Abstract

We introduce a parametrization of the coupling constant space of the generalized Kontsevich models in terms of a set of moments equivalent to those introduced recently in the context of topological gravity. For the simplest generalization of the Kontsevich model we express the moments as elementary functions of the susceptibilities and the eigenvalues of the external field. We furthermore use the moment technique to derive a closed expression for the genus zero multi-loop correlators for $(3,3m-1)$ and $(3,3m-2)$ rational matter fields coupled to gravity. We comment on the relation between the two-matrix model and the generalized Kontsevich models

14 pages, SPhT/94-102

References in corpus (7)

• Matrix Model Calculations beyond the Spherical Limit
• Towards unified theory of $2d$ gravity
• Rational Theories of 2D Gravity from the Two-Matrix Model
• Strings with Discrete Target Space
• Combinatorial Solution of the Two-Matrix Model
• The Large-$N$ Limit of the Two-Hermitian-matrix model by the hidden BRST method
• From 1-matrix model to Kontsevich model

Cited by in corpus (7)

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• Partition Functions of Matrix Models as the First Special Functions of String Theory. II. Kontsevich Model
• Open/Closed String Duality for Topological Gravity with Matter
• Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models
• Stokes Phenomena and Quantum Integrability in Non-critical String/M Theory
• An algebraic approach to a quartic analogue of the Kontsevich model
• Fractional-Superstring Amplitudes, Multi-Cut Matrix Models and Non-Critical M Theory