Titlebook: Random Surfaces and Quantum Gravity; Orlando Alvarez,Enzo Marinari,Paul Windey Book 1991 Springer Science+Business Media New York 1991 Gra

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Non-Perturbative Effects in 2D Gravity and Matrix Modelsl 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/. expansion of some zero-dimensional matrix model [1]. The . = ∞ limit exhibits critical points which can be shown to describe the continuum limit of 2-dimensional gr

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Topological Strings and Loop Equationsal metric that is introduced to achieve invariance under general coordinate transformations. Even in two-dimensions, where the issue seems much more accessible and essentially reduces to an understanding of the Liouville dynamics, an exact solution of quantum gravity has until recently remained elus

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Action Principle and Large Order Behavior of Non-Perturbative Gravitygravity coupled to . < 1 matter. Our motivation is to learn what we can about non-perturbative features of quantum gravity and string theory using standard mathematical techniques for studying the asymptotic behavior of perturbation series. In particular we wish ultimately to probe whether we indeed

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- Geometryolume cover this subject, rather than paraphrasing our paper, I thought it would be more appropriate to discuss here some investigations carried in collaboration with P. Di Francesco and J.-B. Zuber on the relation between geometry, differential operators and classical . - algebras. The latter were

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Matrix Models of 2D Gravity and Isomonodromic Deformationandles with a weight defined by the Einstein-Hilbert action . is the cosmological constant and . is Newton’s constant, or, equivalently, the string coupling) together with the partition function of some 2D quantum field theory, .(..). The parameters .. are coordinates on a subspace of the space of 2

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The Strength of Nonperturbative Effects in String Theoryupling constant. This is the case in the exactly soluble matrix models. These effects are in principle much larger than the .(—./... effects typical of the low energy field theory. We argue that this behavior should be generic in string theory because string perturbation theory generically behaves l

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Approximating the Critical String Measure Using Dynamically Triangulated Surfaces formulation), reveals an interesting thermodynamical limit. In this limit certain singularities (i.e. critical exponents) appear, signalling a phase transition beyond which one may hope for a non-perturbative description of the theory.

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Matrix Models, String Field Theory and Topologyons of simple string models (more properly: resummation of the perturbation series around simple solutions of the classical string equations of motion). These models all have one and two dimensional target spaces, a fact directly connected to their solubility. Indeed, it is easy to show that all of