Superintegrability and Kontsevich-Hermitian relation

TL;DR

This paper explores the relationship between Kontsevich-Penner and Hermitian matrix models through superintegrability, providing new insights into their equivalence and implications for model deformations.

Contribution

It offers a detailed analysis of superintegrability relations in matrix models, clarifying the equivalence and extending it to deformed models like Brezin-Hikami.

Findings

Explicit formulas for character averages in matrix models.

Simplification of the Brezin-Hikami extension.

Enhanced understanding of model deformations.

Abstract

We analyze the well-known equivalence between the quadratic Kontsevich-Penner and Hermitian matrix models from the point of view of superintegrability relations, i.e. explicit formulas for character averages. This is not that trivial on the Kontsevich side and seems important for further studies of various deformations of Kontsevich models. In particular, the Brezin-Hikami extension of the above equivalence becomes straightforward.