Loop Equations and Virasoro Constraints in Matrix Models

Details Loop Equations and Virasoro Constraints in Matrix Models Loop Equations and Virasoro Constraints in Matrix Models

1991-12-19

arxiv.org/abs/hep-th/9112058v1

Physics

High Energy Physics

High Energy Physics - Theory

22 pages. Talk at XXVth International Symposium on the Theory of Elementary Particles, G\"osen, Germany, September 23--26

Scientific paper

In the first part of the talk, I review the applications of loop equations to the matrix models and to 2-dimensional quantum gravity which is defined as their continuum limit. The results concerning multi-loop correlators for low genera and the Virasoro invariance are discussed. The second part is devoted to the Kontsevich matrix model which is equivalent to 2-dimensional topological gravity. I review the Schwinger--Dyson equations for the Kontsevich model as well as their explicit solution in genus zero. The relation between the Kontsevich model and the continuum limit of the hermitean one-matrix model is discussed.

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