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

TL;DR

This paper derives Virasoro constraints for the Kontsevich model and extends the approach to unitary matrices, introducing new constraints and discussing solutions for symmetric matrices in an external field.

Contribution

It provides a simplified derivation of Virasoro constraints and generalizes the method to unitary matrices, revealing new constraints and solution strategies.

Findings

Derived Virasoro constraints for the Kontsevich model

Extended constraints to unitary matrix models

Discussed solutions for symmetric matrices in external fields

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.