Generating functions in two-dimensional quantum gravity |
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| Affiliation: | 1. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada;2. Department of Mathematics, Anand International College of Engineering, Jaipur 303012, Rajasthan, India;3. Department of Mathematics, Poornima College of Engineering, Jaipur 302002, Rajasthan, India;1. Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, United States of America;2. Department of Mathematics, Wellesley College, Wellesley, MA 02481, United States of America;3. Department of Mathematics, University of Chicago, Chicago, IL 60637, United States of America;4. Department of Mathematics, Princeton University, Princeton, NJ 08544, United States of America;5. Department of Mathematics, Stanford University, Stanford, CA 94305, United States of America |
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| Abstract: | We solve general 1-matrix models without taking the double scaling limit. A method of computing generating functions is presented. We calculate the generating functions for a simple and a double torus. Our method is also applicable to higher genus. Each generating function can be expressed by a “specific heat” function for the sphere. Universal terms, which survived in the double scaling limit can be easily picked out from our exact solutions. We also find that the regular part of the spherical generating function is at most bilinear in the coupling constants of the source terms. |
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