Emergent Geometry of Matrix Models with Even Couplings

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.