Unitary And Hermitian Matrices In An External Field II: The Kontsevich Model And Continuum Virasoro Constraints

Abstract

We give a simple derivation of the Virasoro constraints in the Kontsevich model, first derived by Witten. We generalize the method to a model of unitary matrices, for which we find a new set of Virasoro constraints. Finally we discuss the solution for symmetric matrices in an external field.

17 pages

References in corpus (4)

• Towards unified theory of $2d$ gravity
• Unification of All String Models with $c<1$
• On Equivalence of Topological and Quantum 2d Gravity
• Hermitian vs. Anti-Hermitian 1-Matrix Models and Their Hierarchies

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