Loop Equations and Virasoro Constraints in Matrix Models
High Energy Physics - Theory
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.hep-th/9112058,
title = {Loop Equations and Virasoro Constraints in Matrix Models},
author = {Yu. Makeenko},
journal= {arXiv preprint arXiv:hep-th/9112058},
year = {2007}
}
Comments
22 pages. Talk at XXVth International Symposium on the Theory of Elementary Particles, G\"osen, Germany, September 23--26