Quantization of Harer-Zagier formulas

TL;DR

This paper extends the Harer-Zagier formulas to q-deformed Hermitian Gaussian matrix models, providing a comprehensive description of correlators and paving the way for q-deformed matrix model properties.

Contribution

It introduces q-analogues of Harer-Zagier formulas for matrix model correlators, enabling analysis of q-deformations of key matrix model features.

Findings

Derived q-analogues of Harer-Zagier formulas for correlators

Fully described single-trace correlators in q-deformed models

Opened pathways for studying q-deformations of genus expansion and Wick theorem

Abstract

We derive the analogues of the Harer-Zagier formulas for single- and double-trace correlators in the q-deformed Hermitian Gaussian matrix model. This fully describes single-trace correlators and opens a road to $q$-deformations of important matrix models properties, such as genus expansion and Wick theorem.