Random Surfaces and Quantum Gravity

✍ Scribed by Orlando Alvarez, Paul Windey (auth.), Orlando Alvarez, Enzo Marinari, Paul Windey (eds.)

• Publisher: Springer US
• Year: 1991
• Tongue: English
• Leaves: 400
• Series: NATO ASI Series 262
• Edition: 1
• Category: Library

✦ Synopsis

The Cargese Workshop Random Surfaces and Quantum Gravity was held from May 27 to June 2, 1990. Little was known about string theory in the non-perturbative regime before Oetober 1989 when non-perturbative equations for the string partition functions were found by using methods based on the random triangulations of surfaees. This set of methods pro­ vides a deseription of non-eritical string theory or equivalently of the coupling of matter fields to quantum gravity in two dimensions. The Cargese meeting was very successful in that it provided the first opportunity to gather most of the active workers in the field for a fuH week of lectures and extensive informal discussions about these exeiting new developments. The main results were reviewed, recent advances were explained, new results and conjectures (which appear for the first time in these proceedings) were presented and discussed. Among the most important topics discussed at the workshop were: The relation of KdV theory to loop equations and the Virasoro algebra, new results in Liouville field theory, effective (1 + 1) dimensional theory for 2 - D quantum gravity coupled to c = 1 matter and its fermionization, proposal for a new geometrical interpretation of the string equation and possible definition of quantum Riemann surfaces, discussion of the string equation for the multi-matrix models, links with topological field theories of gravity, issues in using target space supersymmetry to define good theories, definition of the partition function via analytic continuation, new models of random surfaces

✦ Table of Contents

Front Matter....Pages i-viii
Diffusion Equation, Continuum Limit and Universality in Two Dimensional Quantum Gravity....Pages 1-10
On Triangles and Squares....Pages 11-19
Non-Perturbative Effects in 2D Gravity and Matrix Models....Pages 21-33
Integrable Models of Two Dimensional Quantum Gravity....Pages 35-51
Topological Strings and Loop Equations....Pages 53-76
The Two-Matrix Model....Pages 77-83
Action Principle and Large Order Behavior of Non-Perturbative Gravity....Pages 85-109
W - Geometry....Pages 111-133
Strings Embedded in Dynkin Diagrams....Pages 135-149
Phase Transitions in One Matrix Models....Pages 151-156
Matrix Models of 2D Gravity and Isomonodromic Deformation....Pages 157-190
The Strength of Nonperturbative Effects in String Theory....Pages 191-200
Approximating the Critical String Measure Using Dynamically Triangulated Surfaces....Pages 201-215
Matrix Models, String Field Theory and Topology....Pages 217-235
Multipoint Correlation Functions in One-Dimensional String Theory....Pages 237-241
The Penner Model and D = 1 String Theory....Pages 243-253
Non-Perturbative String Theory....Pages 255-267
Bosonic Strings and String Field Theories in One-Dimensional Target Space....Pages 269-306
A Few Remarks on Low Dimensional String Theory....Pages 307-315
Excitations and Interactions in a One Dimensional String Theory....Pages 317-326
Random Surfaces in Dimensions Larger than One....Pages 327-336
On Gauge Invariances in Stochastic Quantization....Pages 337-346
The Quantum Group Structure of Quantum Gravity in Two Dimensions....Pages 347-361
Notes on Quantum Liouville Theory and Quantum Gravity....Pages 363-395
Back Matter....Pages 397-407

✦ Subjects

Astronomy, Observations and Techniques;Classical and Quantum Gravitation, Relativity Theory;Theoretical, Mathematical and Computational Physics