Loop Equations and Virasoro Constraints in Matrix Models

Yu. Makeenko

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arXiv · hep-th/9112058

Loop Equations and Virasoro Constraints in Matrix Models

Yu. Makeenko

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Abstract

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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Yu. Makeenko. 1991-12-19. Loop Equations and Virasoro Constraints in Matrix Models. https://arxiv.org/abs/hep-th/9112058

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