Non-Perturbative Effects in 2D Gravity and Matrix Models

  • François David
Chapter
Part of the NATO ASI Series book series (NSSB, volume 262)

Abstract

Two dimensional Euclidean quantum gravity may be formulated as a functional integral over 2-dimensional Riemannian manifolds. This infinite dimensional integral may be discretized in such a way that the topological expansion in terms of the genus of the manifold is mapped onto the 1/N expansion of some zero-dimensional matrix model [1]. The N = ∞ limit exhibits critical points which can be shown to describe the continuum limit of 2-dimensional gravity on a genus zero manifold, eventually coupled to some matter fields. Recently it was shown that a scaling limit can be constructed [2]. In this limit all the terms of the topological expansion survive and thus one obtains a fully non-perturbative solution for two dimensional gravity. However in the most interesting cases, in particular for pure gravity, the solution is defined as a solution of a non-linear differential equation of the Painlevé type and presents some non-perturbative ambiguities, related to the delicate issue of boundary conditions, which are usually attributed to some “non-perturbative effects” of the theory.

Keywords

Matrix Model Loop Operator Double Polis String Equation Loop Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • François David
    • 1
  1. 1.Service de Physique ThéoriqueCEN SaclayGif sur Yvette CedexFrance

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