Emergent Geometry of Matrix Models with Even Couplings

TL;DR

This paper demonstrates that the modified GUE matrix model with even couplings produces correlation functions satisfying topological recursion and relates to intersection numbers on moduli spaces, revealing deep geometric structures.

Contribution

It establishes a connection between the modified GUE partition function with even couplings and Eynard-Orantin topological recursion, linking matrix models to algebraic geometry.

Findings

Correlation functions satisfy Eynard-Orantin recursion

Relation to intersection numbers on moduli spaces

Extension to arbitrary genera

Abstract

We show that to the modified GUE partition function with even coupling introduced by Dubrovin, Liu, Yang and Zhang, one can associate $n$-point correlation functions in arbitrary genera which satisfy Eynard-Orantin topological recursions. Furthermore, these $n$-point functions are related to intersection numbers on the Deligne-Mumford moduli spaces.